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| <p>SQL functions for evaluating probability functions. |
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| Functions</h2></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aea21a931dc5578a570e3370af3d8d43a">bernoulli_cdf</a> (float8 x, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Bernoulli cumulative distribution function. <a href="#aea21a931dc5578a570e3370af3d8d43a"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a434b3ad1f3964835834dc2a942b820ef">bernoulli_pmf</a> (int4 x, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Bernoulli probability mass function. <a href="#a434b3ad1f3964835834dc2a942b820ef"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a7133c2e86fd2f6384416ee0e4fd3a60b">bernoulli_quantile</a> (float8 p, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Bernoulli quantile function. <a href="#a7133c2e86fd2f6384416ee0e4fd3a60b"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a72e1cca872da35592075dbcfb18aed3f">beta_cdf</a> (float8 x, float8 alpha, float8 beta)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Beta cumulative distribution function. <a href="#a72e1cca872da35592075dbcfb18aed3f"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aa105049e6e3bb9b3891b0ed1b343e28e">beta_pdf</a> (float8 x, float8 alpha, float8 beta)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Beta probability density function. <a href="#aa105049e6e3bb9b3891b0ed1b343e28e"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a32433aa742c0504d33e98e28a3e2f190">beta_quantile</a> (float8 p, float8 alpha, float8 beta)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Beta quantile function. <a href="#a32433aa742c0504d33e98e28a3e2f190"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aa5000bad6e2e4af1c8cbfec7ea884476">binomial_cdf</a> (float8 x, int4 n, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Binomial cumulative distribution function. <a href="#aa5000bad6e2e4af1c8cbfec7ea884476"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aa0614475b8685bf8e37533d2ac5bb116">binomial_pmf</a> (int4 x, int4 n, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Binomial probability mass function. <a href="#aa0614475b8685bf8e37533d2ac5bb116"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a49f421c58d2e1abd63b83d71af9edf21">binomial_quantile</a> (float8 p, int4 n, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Binomial quantile function. <a href="#a49f421c58d2e1abd63b83d71af9edf21"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a2d8874c2a5679403a473bfedb14467a4">cauchy_cdf</a> (float8 x, float8 location, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Cauchy cumulative distribution function. <a href="#a2d8874c2a5679403a473bfedb14467a4"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aebfad9365a7fc7a553c3b5c7931f2450">cauchy_pdf</a> (float8 x, float8 location, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Cauchy probability density function. <a href="#aebfad9365a7fc7a553c3b5c7931f2450"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ae8aa9b741e89c8d9236a682d218006e0">cauchy_quantile</a> (float8 p, float8 location, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Cauchy quantile function. <a href="#ae8aa9b741e89c8d9236a682d218006e0"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a230513b6b549d5b445cbacbdbab42c15">chi_squared_cdf</a> (float8 x, float8 df)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Chi-squared cumulative distribution function. <a href="#a230513b6b549d5b445cbacbdbab42c15"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a90bccc717d7052e83bafd7f160a783b1">chi_squared_pdf</a> (float8 x, float8 df)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Chi-squared distribution probability density function. <a href="#a90bccc717d7052e83bafd7f160a783b1"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ad125307fe65a33b60f6dd524037d4548">chi_squared_quantile</a> (float8 p, float8 df)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Chi-squared distribution quantile function. <a href="#ad125307fe65a33b60f6dd524037d4548"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a6d1bf6816f56b8e5ba6bf6ca94752f46">exponential_cdf</a> (float8 x, float8 lambda)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Exponential cumulative distribution function. <a href="#a6d1bf6816f56b8e5ba6bf6ca94752f46"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a18a5458c4bc85f0c4ea321317f90bdbb">exponential_pdf</a> (float8 x, float8 lambda)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Exponential probability density function. <a href="#a18a5458c4bc85f0c4ea321317f90bdbb"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ae3687b8e69a402154b829a6531b1b279">exponential_quantile</a> (float8 p, float8 lambda)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Exponential quantile function. <a href="#ae3687b8e69a402154b829a6531b1b279"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#acffffe04c15eccd2e88cdac250bccc68">extreme_value_cdf</a> (float8 x, float8 location, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Extreme Value cumulative distribution function. <a href="#acffffe04c15eccd2e88cdac250bccc68"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a03a3494462f4cb8c9fb6212e72b0b2e9">extreme_value_pdf</a> (float8 x, float8 location, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Extreme Value probability density function. <a href="#a03a3494462f4cb8c9fb6212e72b0b2e9"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aeb5a7d295b83a891774a4fb0ef27c458">extreme_value_quantile</a> (float8 p, float8 location, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Extreme Value quantile function. <a href="#aeb5a7d295b83a891774a4fb0ef27c458"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a6c5b3e35531e44098f9d0cbef14cb8a6">fisher_f_cdf</a> (float8 x, float8 df1, float8 df2)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Fisher F cumulative distribution function. <a href="#a6c5b3e35531e44098f9d0cbef14cb8a6"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a1c7937426379a8913519a6abc5a38ac2">fisher_f_pdf</a> (float8 x, float8 df1, float8 df2)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Fisher F probability density function. <a href="#a1c7937426379a8913519a6abc5a38ac2"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ab6ed888a5338a0bee9c55edf4d33847f">fisher_f_quantile</a> (float8 p, float8 df1, float8 df2)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Fisher F quantile function. <a href="#ab6ed888a5338a0bee9c55edf4d33847f"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ab6760b0486bad2f1ab0635eb59404e7c">gamma_cdf</a> (float8 x, float8 shape, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Gamma cumulative distribution function. <a href="#ab6760b0486bad2f1ab0635eb59404e7c"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a6c37e3bda2596accbb46525321a328c4">gamma_pdf</a> (float8 x, float8 shape, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Gamma probability density function. <a href="#a6c37e3bda2596accbb46525321a328c4"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ac48bbd491bd34831415705c3a0b7bf29">gamma_quantile</a> (float8 p, float8 shape, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Gamma quantile function. <a href="#ac48bbd491bd34831415705c3a0b7bf29"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a00879bdf7d48ceddedb3b4cc33511497">geometric_cdf</a> (float8 x, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Geometric cumulative distribution function. <a href="#a00879bdf7d48ceddedb3b4cc33511497"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a5e08db93bd448a1e2164e106ce5781a4">geometric_pmf</a> (int4 x, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Geometric probability mass function. <a href="#a5e08db93bd448a1e2164e106ce5781a4"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a62674ca958aec0533cdf0a74a1dadea9">geometric_quantile</a> (float8 p, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Geometric quantile function. <a href="#a62674ca958aec0533cdf0a74a1dadea9"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a5c48e7fa2fc7bcbc69c7f4da663d457f">hypergeometric_cdf</a> (float8 x, int4 r, int4 n, int4 N)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Hypergeometric cumulative distribution function. <a href="#a5c48e7fa2fc7bcbc69c7f4da663d457f"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#afbd2f8d9fb30fb179f59cc14f1fd8d6d">hypergeometric_pmf</a> (int4 x, int4 r, int4 n, int4 N)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Hypergeometric probability mass function. <a href="#afbd2f8d9fb30fb179f59cc14f1fd8d6d"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a813cc27fe097e797ed0fb6022c7bb79a">hypergeometric_quantile</a> (float8 p, int4 r, int4 n, int4 N)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Hypergeometric quantile function. <a href="#a813cc27fe097e797ed0fb6022c7bb79a"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a85e9c16aa2c6973ddeb7883a5f153d93">inverse_gamma_cdf</a> (float8 x, float8 shape, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Inverse Gamma cumulative distribution function. <a href="#a85e9c16aa2c6973ddeb7883a5f153d93"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a126211c2172a43a654288fa72a2349f9">inverse_gamma_pdf</a> (float8 x, float8 shape, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Inverse Gamma probability density function. <a href="#a126211c2172a43a654288fa72a2349f9"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a5876aae01f14729866d4fd52918a65ba">inverse_gamma_quantile</a> (float8 p, float8 shape, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Inverse Gamma quantile function. <a href="#a5876aae01f14729866d4fd52918a65ba"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aeef43f74f583bdff17bd074d9c0d9607">kolmogorov_cdf</a> (float8 x)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Kolmogorov cumulative distribution function. <a href="#aeef43f74f583bdff17bd074d9c0d9607"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a64e197de8da3761acdeec9db7e211703">laplace_cdf</a> (float8 x, float8 mean, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Laplace cumulative distribution function. <a href="#a64e197de8da3761acdeec9db7e211703"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a750278ad29d514793f76e159b773f410">laplace_pdf</a> (float8 x, float8 mean, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Laplace probability density function. <a href="#a750278ad29d514793f76e159b773f410"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a77f94fc43d4777fc4f68d18e29454a81">laplace_quantile</a> (float8 p, float8 mean, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Laplace quantile function. <a href="#a77f94fc43d4777fc4f68d18e29454a81"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a140f674876813d5e786a4d8ba8d75c87">logistic_cdf</a> (float8 x, float8 mean, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Logistic cumulative distribution function. <a href="#a140f674876813d5e786a4d8ba8d75c87"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#afa38eb6c61d3c9825d5c172e6c17dbf7">logistic_pdf</a> (float8 x, float8 mean, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Logistic probability density function. <a href="#afa38eb6c61d3c9825d5c172e6c17dbf7"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a5a77a0bc5884af2a914a955174892ae2">logistic_quantile</a> (float8 p, float8 mean, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Logistic quantile function. <a href="#a5a77a0bc5884af2a914a955174892ae2"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a4c05b347f8feb64e1236d21b850af61e">lognormal_cdf</a> (float8 x, float8 location, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Log-normal cumulative distribution function. <a href="#a4c05b347f8feb64e1236d21b850af61e"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a7370b797bf450f9aa54d4fea4d64d611">lognormal_pdf</a> (float8 x, float8 location, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Log-normal probability density function. <a href="#a7370b797bf450f9aa54d4fea4d64d611"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aab3a6de990ae5a81834274a1cf9cad8f">lognormal_quantile</a> (float8 p, float8 location, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Log-normal quantile function. <a href="#aab3a6de990ae5a81834274a1cf9cad8f"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ad0a7e4474f828869fb90e62f8e6f04d7">negative_binomial_cdf</a> (float8 x, float8 r, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Negative binomial cumulative distribution function. <a href="#ad0a7e4474f828869fb90e62f8e6f04d7"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ab9cbc30424eba30f2df2a32a7e45f138">negative_binomial_pmf</a> (int4 x, float8 r, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Negative binomial probability mass function. <a href="#ab9cbc30424eba30f2df2a32a7e45f138"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ad9e541de8b41da2e7b7434f862db4845">negative_binomial_quantile</a> (float8 p, float8 r, float8 sp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Negative binomial quantile function. <a href="#ad9e541de8b41da2e7b7434f862db4845"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a1361569bd86e41f796c70f8cb277010e">non_central_beta_cdf</a> (float8 x, float8 alpha, float8 beta, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral beta cumulative distribution function. <a href="#a1361569bd86e41f796c70f8cb277010e"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ad4a12c083054f0e2d316ae76c9aaeef7">non_central_beta_pdf</a> (float8 x, float8 alpha, float8 beta, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral beta probability density function. <a href="#ad4a12c083054f0e2d316ae76c9aaeef7"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a3073b409eaee3faa6d43df014662c279">non_central_beta_quantile</a> (float8 p, float8 alpha, float8 beta, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral beta quantile function. <a href="#a3073b409eaee3faa6d43df014662c279"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ab4b7d2cf10bb031328dcc34c6ff494ad">non_central_chi_squared_cdf</a> (float8 x, float8 df, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral chi-squared cumulative distribution function. <a href="#ab4b7d2cf10bb031328dcc34c6ff494ad"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aa7a563183224593d1e0d623a3c5489d8">non_central_chi_squared_pdf</a> (float8 x, float8 df, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral chi-squared distribution probability density function. <a href="#aa7a563183224593d1e0d623a3c5489d8"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ad694e29187b629ae683ef1235d2b9270">non_central_chi_squared_quantile</a> (float8 p, float8 df, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral chi-squared distribution quantile function. <a href="#ad694e29187b629ae683ef1235d2b9270"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a00051df630007b530ce86b4ab44a0434">non_central_f_cdf</a> (float8 x, float8 df1, float8 df2, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral Fisher F cumulative distribution function. <a href="#a00051df630007b530ce86b4ab44a0434"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a3d94edcf90fca1fa52671293a9ea9c2f">non_central_f_pdf</a> (float8 x, float8 df1, float8 df2, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral Fisher F probability density function. <a href="#a3d94edcf90fca1fa52671293a9ea9c2f"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a92b2a978db480a6c78cfb708107ecb92">non_central_f_quantile</a> (float8 p, float8 df1, float8 df2, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral Fisher F quantile function. <a href="#a92b2a978db480a6c78cfb708107ecb92"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#afaf4374d2720b230a54713e21ecb1955">non_central_t_cdf</a> (float8 x, float8 df, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral Student-t cumulative distribution function. <a href="#afaf4374d2720b230a54713e21ecb1955"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a4799e3bb68a496d9bc1ef1ea85265409">non_central_t_pdf</a> (float8 x, float8 df, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral Student-t probability density function. <a href="#a4799e3bb68a496d9bc1ef1ea85265409"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#af50865aba2ece2e23b2af461a02f7d12">non_central_t_quantile</a> (float8 p, float8 df, float8 ncp)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Noncentral Student-t quantile function. <a href="#af50865aba2ece2e23b2af461a02f7d12"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aebcd34ad7b1ca4b31d9699112c9a3b90">normal_cdf</a> (float8 x, float8 mean=0, float8 sd=1)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Normal cumulative distribution function. <a href="#aebcd34ad7b1ca4b31d9699112c9a3b90"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a63f555f36385d86e229cdca223e39567">normal_pdf</a> (float8 x, float8 mean=0, float8 sd=1)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Normal probability density function. <a href="#a63f555f36385d86e229cdca223e39567"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a53d56b672fe4cd1277cb5eac5de5118f">normal_quantile</a> (float8 p, float8 mean=0, float8 sd=1)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Normal quantile function. <a href="#a53d56b672fe4cd1277cb5eac5de5118f"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aa1a42ebd68f20f65bc1784b427721b5d">pareto_cdf</a> (float8 x, float8 scale, float8 shape)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Pareto cumulative distribution function. <a href="#aa1a42ebd68f20f65bc1784b427721b5d"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a22c56a6e48bc442435b13afac2a1eb37">pareto_pdf</a> (float8 x, float8 scale, float8 shape)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Pareto probability density function. <a href="#a22c56a6e48bc442435b13afac2a1eb37"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a77779e2b5fa951189ccba6806c503c4d">pareto_quantile</a> (float8 p, float8 scale, float8 shape)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Pareto quantile function. <a href="#a77779e2b5fa951189ccba6806c503c4d"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ae0b4313d9fe730d6efb3f7c44206f345">poisson_cdf</a> (float8 x, float8 mean)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Poisson cumulative distribution function. <a href="#ae0b4313d9fe730d6efb3f7c44206f345"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a82f1edc27261021c73cd080ff2677a9f">poisson_pmf</a> (int4 x, float8 mean)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Poisson probability mass function. <a href="#a82f1edc27261021c73cd080ff2677a9f"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a032d26db18b2ee1034085f5521939c61">poisson_quantile</a> (float8 p, float8 mean)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Poisson quantile function. <a href="#a032d26db18b2ee1034085f5521939c61"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aab0ddb8a5348cfa387d777043a3cb6d0">rayleigh_cdf</a> (float8 x, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Rayleigh cumulative distribution function. <a href="#aab0ddb8a5348cfa387d777043a3cb6d0"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a798541736d9255bdd5c0bd94924d47bc">rayleigh_pdf</a> (float8 x, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Rayleigh probability density function. <a href="#a798541736d9255bdd5c0bd94924d47bc"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#acd6757acab1683c735e2b57901494336">rayleigh_quantile</a> (float8 p, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Rayleigh quantile function. <a href="#acd6757acab1683c735e2b57901494336"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a5322531131074c23a2dbf067ee504ef7">students_t_cdf</a> (float8 x, float8 df)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Student's t cumulative distribution function. <a href="#a5322531131074c23a2dbf067ee504ef7"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a8815c21670fff9d31946553a84b845b1">students_t_pdf</a> (float8 x, float8 df)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Student's t probability density function. <a href="#a8815c21670fff9d31946553a84b845b1"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a7d64add02af21a95d73502b2dd466a75">students_t_quantile</a> (float8 p, float8 df)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Student's t quantile function. <a href="#a7d64add02af21a95d73502b2dd466a75"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#abf9c7d870bcfe68cacaa421749bbdf35">triangular_cdf</a> (float8 x, float8 lower, float8 mode, float8 upper)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Triangular cumulative distribution function. <a href="#abf9c7d870bcfe68cacaa421749bbdf35"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a0c511b9748b2f7a21fe56aaf5f66d188">triangular_pdf</a> (float8 x, float8 lower, float8 mode, float8 upper)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Triangular probability density function. <a href="#a0c511b9748b2f7a21fe56aaf5f66d188"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a4777540ab1b003ff92d484c4bc26af27">triangular_quantile</a> (float8 p, float8 lower, float8 mode, float8 upper)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Triangular quantile function. <a href="#a4777540ab1b003ff92d484c4bc26af27"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aa3a05f4f2e0ef9eb65e828261ecfbed9">uniform_cdf</a> (float8 x, float8 lower, float8 upper)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Uniform cumulative distribution function. <a href="#aa3a05f4f2e0ef9eb65e828261ecfbed9"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#ab90fa34d90a9c75747a34c3f210df239">uniform_pdf</a> (float8 x, float8 lower, float8 upper)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Uniform probability density function. <a href="#ab90fa34d90a9c75747a34c3f210df239"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a629587a0fdefb588d28b15517ae5cc04">uniform_quantile</a> (float8 p, float8 lower, float8 upper)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Uniform quantile function. <a href="#a629587a0fdefb588d28b15517ae5cc04"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a50e4a1883588cd7a4c1ff1017399e4af">weibull_cdf</a> (float8 x, float8 shape, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Weibull cumulative distribution function. <a href="#a50e4a1883588cd7a4c1ff1017399e4af"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#a81a876ae2b8598f060dadb179b9324d2">weibull_pdf</a> (float8 x, float8 shape, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Weibull probability density function. <a href="#a81a876ae2b8598f060dadb179b9324d2"></a><br/></td></tr> |
| <tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="prob_8sql__in.html#aa544631ddeb7a5c06b995b4383c3b612">weibull_quantile</a> (float8 p, float8 shape, float8 scale)</td></tr> |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">Weibull quantile function. <a href="#aa544631ddeb7a5c06b995b4383c3b612"></a><br/></td></tr> |
| </table> |
| <hr/><a name="details" id="details"></a><h2>Detailed Description</h2> |
| <div class="textblock"><dl class="see"><dt><b>See also:</b></dt><dd>For an overview of probability functions, see the module description <a class="el" href="group__grp__prob.html">Probability Functions</a>. </dd></dl> |
| |
| <p>Definition in file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| </div><hr/><h2>Function Documentation</h2> |
| <a class="anchor" id="aea21a931dc5578a570e3370af3d8d43a"></a><!-- doxytag: member="prob.sql_in::bernoulli_cdf" ref="aea21a931dc5578a570e3370af3d8d43a" args="(float8 x, float8 sp)" --> |
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| <td class="memname">float8 bernoulli_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( p \in [0,1] \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a Bernoulli-distributed random variable with success probability \( \mathit{sp} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00138">138</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a434b3ad1f3964835834dc2a942b820ef"></a><!-- doxytag: member="prob.sql_in::bernoulli_pmf" ref="a434b3ad1f3964835834dc2a942b820ef" args="(int4 x, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 bernoulli_pmf </td> |
| <td>(</td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in [0,1] \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability mass function of a Bernoulli-distributed random variable with success probability \( \mathit{sp} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00155">155</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a7133c2e86fd2f6384416ee0e4fd3a60b"></a><!-- doxytag: member="prob.sql_in::bernoulli_quantile" ref="a7133c2e86fd2f6384416ee0e4fd3a60b" args="(float8 p, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 bernoulli_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in [0,1] \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>0 if \( p \leq 1 - \mathit{sp} \) and 1 otherwise </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00170">170</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a72e1cca872da35592075dbcfb18aed3f"></a><!-- doxytag: member="prob.sql_in::beta_cdf" ref="a72e1cca872da35592075dbcfb18aed3f" args="(float8 x, float8 alpha, float8 beta)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 beta_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>alpha</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>beta</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">alpha</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">beta</td><td>Shape \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a beta distributed random variable with shape parameters \( \alpha \) and \( \beta \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00188">188</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aa105049e6e3bb9b3891b0ed1b343e28e"></a><!-- doxytag: member="prob.sql_in::beta_pdf" ref="aa105049e6e3bb9b3891b0ed1b343e28e" args="(float8 x, float8 alpha, float8 beta)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 beta_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>alpha</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>beta</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">alpha</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">beta</td><td>Shape \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a beta random variable with shape parameters \( \alpha \) and \( \beta \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00207">207</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a32433aa742c0504d33e98e28a3e2f190"></a><!-- doxytag: member="prob.sql_in::beta_quantile" ref="a32433aa742c0504d33e98e28a3e2f190" args="(float8 p, float8 alpha, float8 beta)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 beta_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>alpha</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>beta</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">alpha</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">beta</td><td>Shape \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is beta distribution random variable with shape parameters \( \alpha \) and \( \beta \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00226">226</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aa5000bad6e2e4af1c8cbfec7ea884476"></a><!-- doxytag: member="prob.sql_in::binomial_cdf" ref="aa5000bad6e2e4af1c8cbfec7ea884476" args="(float8 x, int4 n, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 binomial_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>n</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">n</td><td>The number of trials \( n \in \mathbb N_0 \) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in [0,1] \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a binomially distributed random variable with \( n \) trials and success probability \( \mathit{sp} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00246">246</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aa0614475b8685bf8e37533d2ac5bb116"></a><!-- doxytag: member="prob.sql_in::binomial_pmf" ref="aa0614475b8685bf8e37533d2ac5bb116" args="(int4 x, int4 n, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 binomial_pmf </td> |
| <td>(</td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>n</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">n</td><td>The number of trials \( n \in \mathbb N_0 \) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in [0,1] \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability mass function of a binomially distributed random variable with \( n \) trials and success probability \( \mathit{sp} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00265">265</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a49f421c58d2e1abd63b83d71af9edf21"></a><!-- doxytag: member="prob.sql_in::binomial_quantile" ref="a49f421c58d2e1abd63b83d71af9edf21" args="(float8 p, int4 n, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 binomial_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>n</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">n</td><td>The number of trials \( n \in \mathbb N_0 \) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in [0,1] \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>If \( p < 0.5 \) the maximum \( x \) such that \( p \geq \Pr[X \leq x] \). If \( p \geq 0.5 \) the minimum \( x \) such that \( p \leq \Pr[X \leq x] \). Here, \( X \) is a binomially distributed random variable with \( n \) trials and success probability \( \mathit{sp} \). </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00286">286</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a2d8874c2a5679403a473bfedb14467a4"></a><!-- doxytag: member="prob.sql_in::cauchy_cdf" ref="a2d8874c2a5679403a473bfedb14467a4" args="(float8 x, float8 location, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 cauchy_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>location</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">location</td><td>Location \( x_0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \gamma > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a Cauchy-distributed random variable with location and scale parameters \( x_0 \) and \( \gamma \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00306">306</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aebfad9365a7fc7a553c3b5c7931f2450"></a><!-- doxytag: member="prob.sql_in::cauchy_pdf" ref="aebfad9365a7fc7a553c3b5c7931f2450" args="(float8 x, float8 location, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 cauchy_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>location</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">location</td><td>Location \( x_0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \gamma > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a Cauchy-distributed random variable with location and scale parameters \( x_0 \) and \( \gamma \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00325">325</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ae8aa9b741e89c8d9236a682d218006e0"></a><!-- doxytag: member="prob.sql_in::cauchy_quantile" ref="ae8aa9b741e89c8d9236a682d218006e0" args="(float8 p, float8 location, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 cauchy_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>location</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">location</td><td>Location \( x_0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \gamma > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Cauchy-distributed random variable with location and scale parameters \( x_0 \) and \( \gamma \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00344">344</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a230513b6b549d5b445cbacbdbab42c15"></a><!-- doxytag: member="prob.sql_in::chi_squared_cdf" ref="a230513b6b549d5b445cbacbdbab42c15" args="(float8 x, float8 df)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 chi_squared_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a chi-squared distributed random variable with \( \nu \) degrees of freedom </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00362">362</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a90bccc717d7052e83bafd7f160a783b1"></a><!-- doxytag: member="prob.sql_in::chi_squared_pdf" ref="a90bccc717d7052e83bafd7f160a783b1" args="(float8 x, float8 df)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 chi_squared_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a chi-squared distributed random variable with \( \nu \) degrees of freedom </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00379">379</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ad125307fe65a33b60f6dd524037d4548"></a><!-- doxytag: member="prob.sql_in::chi_squared_quantile" ref="ad125307fe65a33b60f6dd524037d4548" args="(float8 p, float8 df)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 chi_squared_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \mu > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a chi-squared distributed random variable with \( \nu \) degrees of freedom </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00396">396</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a6d1bf6816f56b8e5ba6bf6ca94752f46"></a><!-- doxytag: member="prob.sql_in::exponential_cdf" ref="a6d1bf6816f56b8e5ba6bf6ca94752f46" args="(float8 x, float8 lambda)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 exponential_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>lambda</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">lambda</td><td>Rate parameter \( \lambda > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is an exponentially distributed random variable with rate parameter \( \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00413">413</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a18a5458c4bc85f0c4ea321317f90bdbb"></a><!-- doxytag: member="prob.sql_in::exponential_pdf" ref="a18a5458c4bc85f0c4ea321317f90bdbb" args="(float8 x, float8 lambda)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 exponential_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>lambda</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">lambda</td><td>Rate parameter \( \lambda > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of exponentially distributed random variable with rate parameter \( \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00430">430</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ae3687b8e69a402154b829a6531b1b279"></a><!-- doxytag: member="prob.sql_in::exponential_quantile" ref="ae3687b8e69a402154b829a6531b1b279" args="(float8 p, float8 lambda)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 exponential_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>lambda</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">lambda</td><td>Rate parameter \( \lambda > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a exponentially distributed random variable with rate parameter \( \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00447">447</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="acffffe04c15eccd2e88cdac250bccc68"></a><!-- doxytag: member="prob.sql_in::extreme_value_cdf" ref="acffffe04c15eccd2e88cdac250bccc68" args="(float8 x, float8 location, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 extreme_value_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>location</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">location</td><td>Location \( \alpha \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is an extreme-value distributed random variable with location and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00466">466</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a03a3494462f4cb8c9fb6212e72b0b2e9"></a><!-- doxytag: member="prob.sql_in::extreme_value_pdf" ref="a03a3494462f4cb8c9fb6212e72b0b2e9" args="(float8 x, float8 location, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 extreme_value_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>location</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">location</td><td>Location \( \alpha \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of an extreme-value distributed random variable with location and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00485">485</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aeb5a7d295b83a891774a4fb0ef27c458"></a><!-- doxytag: member="prob.sql_in::extreme_value_quantile" ref="aeb5a7d295b83a891774a4fb0ef27c458" args="(float8 p, float8 location, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 extreme_value_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>location</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">location</td><td>Location \( \alpha \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is an extreme-value distributed random variable with location and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00504">504</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a6c5b3e35531e44098f9d0cbef14cb8a6"></a><!-- doxytag: member="prob.sql_in::fisher_f_cdf" ref="a6c5b3e35531e44098f9d0cbef14cb8a6" args="(float8 x, float8 df1, float8 df2)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 fisher_f_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df1</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df2</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df1</td><td>Degrees of freedom in numerator \( \nu_1 > 0 \) </td></tr> |
| <tr><td class="paramname">df2</td><td>Degrees of freedom in denominator \( \nu_1 > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a Fisher F-distributed random variable with parameters \( \nu_1 \) and \( \nu_2 \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00523">523</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a1c7937426379a8913519a6abc5a38ac2"></a><!-- doxytag: member="prob.sql_in::fisher_f_pdf" ref="a1c7937426379a8913519a6abc5a38ac2" args="(float8 x, float8 df1, float8 df2)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 fisher_f_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df1</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df2</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df1</td><td>Degrees of freedom in numerator \( \nu_1 > 0 \) </td></tr> |
| <tr><td class="paramname">df2</td><td>Degrees of freedom in denominator \( \nu_1 > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a Fisher F-distributed random variable with parameters \( \nu_1 \) and \( \nu_2 \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00542">542</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ab6ed888a5338a0bee9c55edf4d33847f"></a><!-- doxytag: member="prob.sql_in::fisher_f_quantile" ref="ab6ed888a5338a0bee9c55edf4d33847f" args="(float8 p, float8 df1, float8 df2)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 fisher_f_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df1</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df2</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">df1</td><td>Degrees of freedom in numerator \( \nu_1 > 0 \) </td></tr> |
| <tr><td class="paramname">df2</td><td>Degrees of freedom in denominator \( \nu_1 > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Fisher F-distributed random variable with parameters \( \nu_1 \) and \( \nu_2 \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00561">561</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ab6760b0486bad2f1ab0635eb59404e7c"></a><!-- doxytag: member="prob.sql_in::gamma_cdf" ref="ab6760b0486bad2f1ab0635eb59404e7c" args="(float8 x, float8 shape, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 gamma_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( k > 0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \theta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a gamma distributed random variable with shape and scale parameters \( k \) and \( \theta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00581">581</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a6c37e3bda2596accbb46525321a328c4"></a><!-- doxytag: member="prob.sql_in::gamma_pdf" ref="a6c37e3bda2596accbb46525321a328c4" args="(float8 x, float8 shape, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 gamma_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( k > 0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \theta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a gamma distributed random variable with shape and scale parameters \( k \) and \( \theta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00600">600</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ac48bbd491bd34831415705c3a0b7bf29"></a><!-- doxytag: member="prob.sql_in::gamma_quantile" ref="ac48bbd491bd34831415705c3a0b7bf29" args="(float8 p, float8 shape, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 gamma_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( k > 0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \theta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a gamma distributed random variable with shape and scale parameters \( k \) and \( \theta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00619">619</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a00879bdf7d48ceddedb3b4cc33511497"></a><!-- doxytag: member="prob.sql_in::geometric_cdf" ref="a00879bdf7d48ceddedb3b4cc33511497" args="(float8 x, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 geometric_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in [0,1] \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a geometrically distributed random variable with success probability \( \mathit{sp} \). </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00637">637</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a5e08db93bd448a1e2164e106ce5781a4"></a><!-- doxytag: member="prob.sql_in::geometric_pmf" ref="a5e08db93bd448a1e2164e106ce5781a4" args="(int4 x, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 geometric_pmf </td> |
| <td>(</td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in [0,1] \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability mass function of a geometrically distributed random variable with success probability \( \mathit{sp} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00654">654</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a62674ca958aec0533cdf0a74a1dadea9"></a><!-- doxytag: member="prob.sql_in::geometric_quantile" ref="a62674ca958aec0533cdf0a74a1dadea9" args="(float8 p, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 geometric_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in [0,1] \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>If \( p < 0.5 \) the maximum \( x \) such that \( p \geq \Pr[X \leq x] \). If \( p \geq 0.5 \) the minimum \( x \) such that \( p \leq \Pr[X \leq x] \). Here, \( X \) is a geometrically distributed random variable with success probability \( \mathit{sp} \). </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00673">673</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a5c48e7fa2fc7bcbc69c7f4da663d457f"></a><!-- doxytag: member="prob.sql_in::hypergeometric_cdf" ref="a5c48e7fa2fc7bcbc69c7f4da663d457f" args="(float8 x, int4 r, int4 n, int4 N)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 hypergeometric_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>r</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>n</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>N</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">r</td><td>Number \( r \in \{ 0, 1, \dots, N \} \) of items with distinct property (sometimes called the number of <em>success states</em> in population) </td></tr> |
| <tr><td class="paramname">n</td><td>Number \( n \in \{ 0, 1, \dots, N \} \) of draws (without replacement) </td></tr> |
| <tr><td class="paramname">N</td><td>Total number \( N \in \mathbb N \) of items </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a hypergeometrically distributed random variable with parameters \( r, n, N \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00698">698</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="afbd2f8d9fb30fb179f59cc14f1fd8d6d"></a><!-- doxytag: member="prob.sql_in::hypergeometric_pmf" ref="afbd2f8d9fb30fb179f59cc14f1fd8d6d" args="(int4 x, int4 r, int4 n, int4 N)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 hypergeometric_pmf </td> |
| <td>(</td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>r</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>n</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>N</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">r</td><td>Number \( r \in \{ 0, 1, \dots, N \} \) of items with distinct property (sometimes called the number of <em>success states</em> in population) </td></tr> |
| <tr><td class="paramname">n</td><td>Number \( n \in \{ 0, 1, \dots, N \} \) of draws (without replacement) </td></tr> |
| <tr><td class="paramname">N</td><td>Total number \( N \in \mathbb N \) of items </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability mass function of a hypergeometrically distributed random variable with parameters \( r, n, N \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00722">722</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a813cc27fe097e797ed0fb6022c7bb79a"></a><!-- doxytag: member="prob.sql_in::hypergeometric_quantile" ref="a813cc27fe097e797ed0fb6022c7bb79a" args="(float8 p, int4 r, int4 n, int4 N)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 hypergeometric_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>r</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>n</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>N</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">r</td><td>Number \( r \in \{ 0, 1, \dots, N \} \) of items with distinct property (sometimes called the number of <em>success states</em> in population) </td></tr> |
| <tr><td class="paramname">n</td><td>Number \( n \in \{ 0, 1, \dots, N \} \) of draws (without replacement) </td></tr> |
| <tr><td class="paramname">N</td><td>Total number \( N \in \mathbb N \) of items </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a hypergeometrically distributed random variable with parameters \( r, n, N \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00747">747</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a85e9c16aa2c6973ddeb7883a5f153d93"></a><!-- doxytag: member="prob.sql_in::inverse_gamma_cdf" ref="a85e9c16aa2c6973ddeb7883a5f153d93" args="(float8 x, float8 shape, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 inverse_gamma_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is an inverse-gamma distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00768">768</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a126211c2172a43a654288fa72a2349f9"></a><!-- doxytag: member="prob.sql_in::inverse_gamma_pdf" ref="a126211c2172a43a654288fa72a2349f9" args="(float8 x, float8 shape, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 inverse_gamma_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of an inverse-gamma distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00787">787</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a5876aae01f14729866d4fd52918a65ba"></a><!-- doxytag: member="prob.sql_in::inverse_gamma_quantile" ref="a5876aae01f14729866d4fd52918a65ba" args="(float8 p, float8 shape, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 inverse_gamma_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is an inverse-gamma distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00806">806</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aeef43f74f583bdff17bd074d9c0d9607"></a><!-- doxytag: member="prob.sql_in::kolmogorov_cdf" ref="aeef43f74f583bdff17bd074d9c0d9607" args="(float8 x)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 kolmogorov_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em></td><td>)</td> |
| <td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a Kolmogorov distributed random variable</dd></dl> |
| <dl class="see"><dt><b>See also:</b></dt><dd>Kolmogorov-Smirnov test: <a class="el" href="hypothesis__tests_8sql__in.html#af45ae9d1275d385bbacd18bff688ba7f" title="Perform Kolmogorov-Smirnov test.">ks_test()</a> </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00825">825</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a64e197de8da3761acdeec9db7e211703"></a><!-- doxytag: member="prob.sql_in::laplace_cdf" ref="a64e197de8da3761acdeec9db7e211703" args="(float8 x, float8 mean, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 laplace_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Mean \( \mu \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( b > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a Laplace-distributed random variable with mean \( \mu \) and variance \( 2 b^2 \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00842">842</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a750278ad29d514793f76e159b773f410"></a><!-- doxytag: member="prob.sql_in::laplace_pdf" ref="a750278ad29d514793f76e159b773f410" args="(float8 x, float8 mean, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 laplace_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Mean \( \mu \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( b > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a Laplace-distributed random variable with mean \( \mu \) and variance \( 2 b^2 \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00861">861</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a77f94fc43d4777fc4f68d18e29454a81"></a><!-- doxytag: member="prob.sql_in::laplace_quantile" ref="a77f94fc43d4777fc4f68d18e29454a81" args="(float8 p, float8 mean, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 laplace_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Mean \( \mu \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( b > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Laplace-distributed random variable with mean \( \mu \) and variance \( 2 b^2 \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00880">880</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a140f674876813d5e786a4d8ba8d75c87"></a><!-- doxytag: member="prob.sql_in::logistic_cdf" ref="a140f674876813d5e786a4d8ba8d75c87" args="(float8 x, float8 mean, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 logistic_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Mean \( \mu \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( s > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a logistically distributed random variable with mean \( \mu \) and scale parameter \( s \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00899">899</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="afa38eb6c61d3c9825d5c172e6c17dbf7"></a><!-- doxytag: member="prob.sql_in::logistic_pdf" ref="afa38eb6c61d3c9825d5c172e6c17dbf7" args="(float8 x, float8 mean, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 logistic_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Mean \( \mu \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( s > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a logistically distributed random variable with mean \( \mu \) and scale parameter \( s \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00918">918</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a5a77a0bc5884af2a914a955174892ae2"></a><!-- doxytag: member="prob.sql_in::logistic_quantile" ref="a5a77a0bc5884af2a914a955174892ae2" args="(float8 p, float8 mean, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 logistic_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Mean \( \mu \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( s > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a logistically distributed random variable with mean \( \mu \) and scale parameter \( s \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00937">937</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a4c05b347f8feb64e1236d21b850af61e"></a><!-- doxytag: member="prob.sql_in::lognormal_cdf" ref="a4c05b347f8feb64e1236d21b850af61e" args="(float8 x, float8 location, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 lognormal_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>location</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">location</td><td>Location \( m \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( s > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a lognormally distributed random variable with location and scale parameters \( m \) and \( s \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00957">957</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a7370b797bf450f9aa54d4fea4d64d611"></a><!-- doxytag: member="prob.sql_in::lognormal_pdf" ref="a7370b797bf450f9aa54d4fea4d64d611" args="(float8 x, float8 location, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 lognormal_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>location</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">location</td><td>Location \( m \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( s > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a lognormally distributed random variable with location and scale parameters \( m \) and \( s \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00976">976</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aab3a6de990ae5a81834274a1cf9cad8f"></a><!-- doxytag: member="prob.sql_in::lognormal_quantile" ref="aab3a6de990ae5a81834274a1cf9cad8f" args="(float8 p, float8 location, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 lognormal_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>location</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">location</td><td>Location \( m \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( s > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a lognormally distributed random variable with location and scale parameters \( m \) and \( s \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l00995">995</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ad0a7e4474f828869fb90e62f8e6f04d7"></a><!-- doxytag: member="prob.sql_in::negative_binomial_cdf" ref="ad0a7e4474f828869fb90e62f8e6f04d7" args="(float8 x, float8 r, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 negative_binomial_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>r</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">r</td><td>Total number \( r > 0 \) of successes in \( x + r \) trials (assuming success in the last trial) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in (0,1] \) in each trial </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a negative-binomially distributed random variable with parameters \( r, \mathit{sp} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01015">1015</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ab9cbc30424eba30f2df2a32a7e45f138"></a><!-- doxytag: member="prob.sql_in::negative_binomial_pmf" ref="ab9cbc30424eba30f2df2a32a7e45f138" args="(int4 x, float8 r, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 negative_binomial_pmf </td> |
| <td>(</td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>r</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">r</td><td>Total number \( r > 0 \) of successes in \( x + r \) trials (assuming success in the last trial) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in (0,1] \) in each trial </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability mass function of a negative-binomially distributed random variable with parameters \( r, \mathit{sp} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01035">1035</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ad9e541de8b41da2e7b7434f862db4845"></a><!-- doxytag: member="prob.sql_in::negative_binomial_quantile" ref="ad9e541de8b41da2e7b7434f862db4845" args="(float8 p, float8 r, float8 sp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 negative_binomial_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>r</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">r</td><td>Total number \( r > 0 \) of successes in \( x + r \) trials (assuming success in the last trial) </td></tr> |
| <tr><td class="paramname">sp</td><td>Success probability \( \mathit{sp} \in (0,1] \) in each trial </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>If \( p < 0.5 \) the maximum \( x \) such that \( p \geq \Pr[X \leq x] \). If \( p \geq 0.5 \) the minimum \( x \) such that \( p \leq \Pr[X \leq x] \). Here, \( X \) is a negative-binomially distributed random variable with parameters \( r, \mathit{sp} \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01057">1057</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a1361569bd86e41f796c70f8cb277010e"></a><!-- doxytag: member="prob.sql_in::non_central_beta_cdf" ref="a1361569bd86e41f796c70f8cb277010e" args="(float8 x, float8 alpha, float8 beta, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_beta_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>alpha</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>beta</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">alpha</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">beta</td><td>Shape \( \beta > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>Noncentrality parameter \( \delta \geq 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a noncentral-beta distributed random variable with shape parameters \( shape_1 \) and \( shape_2 \) and noncentrality parameter \( \delta \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01078">1078</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ad4a12c083054f0e2d316ae76c9aaeef7"></a><!-- doxytag: member="prob.sql_in::non_central_beta_pdf" ref="ad4a12c083054f0e2d316ae76c9aaeef7" args="(float8 x, float8 alpha, float8 beta, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_beta_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>alpha</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>beta</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">alpha</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">beta</td><td>Shape \( \beta > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>Noncentrality parameter \( \delta \geq 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a noncentral-beta distributed random variable with shape parameters \( shape_1 \) and \( shape_2 \) and noncentrality parameter \( \delta \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01100">1100</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a3073b409eaee3faa6d43df014662c279"></a><!-- doxytag: member="prob.sql_in::non_central_beta_quantile" ref="a3073b409eaee3faa6d43df014662c279" args="(float8 p, float8 alpha, float8 beta, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_beta_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>alpha</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>beta</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">alpha</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">beta</td><td>Shape \( \beta > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>Noncentrality parameter \( \delta \geq 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a noncentral-beta distributed random variable with shape parameters \( shape_1 \) and \( shape_2 \) and noncentrality parameter \( \delta \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01122">1122</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ab4b7d2cf10bb031328dcc34c6ff494ad"></a><!-- doxytag: member="prob.sql_in::non_central_chi_squared_cdf" ref="ab4b7d2cf10bb031328dcc34c6ff494ad" args="(float8 x, float8 df, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_chi_squared_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>The noncentrality parameter \( \lambda \geq 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a noncentral-chi-squared distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01143">1143</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aa7a563183224593d1e0d623a3c5489d8"></a><!-- doxytag: member="prob.sql_in::non_central_chi_squared_pdf" ref="aa7a563183224593d1e0d623a3c5489d8" args="(float8 x, float8 df, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_chi_squared_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>The noncentrality parameter \( \lambda \geq 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a noncentral-chi-squared distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01162">1162</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ad694e29187b629ae683ef1235d2b9270"></a><!-- doxytag: member="prob.sql_in::non_central_chi_squared_quantile" ref="ad694e29187b629ae683ef1235d2b9270" args="(float8 p, float8 df, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_chi_squared_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>The noncentrality parameter \( \lambda \geq 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a noncentral-chi-squared distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01181">1181</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a00051df630007b530ce86b4ab44a0434"></a><!-- doxytag: member="prob.sql_in::non_central_f_cdf" ref="a00051df630007b530ce86b4ab44a0434" args="(float8 x, float8 df1, float8 df2, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_f_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df1</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df2</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df1</td><td>Degrees of freedom in numerator \( \nu_1 > 0 \) </td></tr> |
| <tr><td class="paramname">df2</td><td>Degrees of freedom in denominator \( \nu_1 > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>The noncentrality parameter \( \lambda \geq 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a noncentral Fisher F-distributed random variable with parameters \( \nu_1, \nu_2, \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01202">1202</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a3d94edcf90fca1fa52671293a9ea9c2f"></a><!-- doxytag: member="prob.sql_in::non_central_f_pdf" ref="a3d94edcf90fca1fa52671293a9ea9c2f" args="(float8 x, float8 df1, float8 df2, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_f_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df1</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df2</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df1</td><td>Degrees of freedom in numerator \( \nu_1 > 0 \) </td></tr> |
| <tr><td class="paramname">df2</td><td>Degrees of freedom in denominator \( \nu_1 > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>The noncentrality parameter \( \lambda \geq 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a noncentral Fisher F-distributed random variable with parameters \( \nu_1, \nu_2, \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01223">1223</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a92b2a978db480a6c78cfb708107ecb92"></a><!-- doxytag: member="prob.sql_in::non_central_f_quantile" ref="a92b2a978db480a6c78cfb708107ecb92" args="(float8 p, float8 df1, float8 df2, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_f_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df1</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df2</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">df1</td><td>Degrees of freedom in numerator \( \nu_1 > 0 \) </td></tr> |
| <tr><td class="paramname">df2</td><td>Degrees of freedom in denominator \( \nu_1 > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>The noncentrality parameter \( \lambda \geq 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a noncentral Fisher F-distributed random variable with parameters \( \nu_1, \nu_2, \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01244">1244</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="afaf4374d2720b230a54713e21ecb1955"></a><!-- doxytag: member="prob.sql_in::non_central_t_cdf" ref="afaf4374d2720b230a54713e21ecb1955" args="(float8 x, float8 df, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_t_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>Noncentrality parameter \( \delta \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a noncentral Student's t-distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \delta \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01265">1265</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a4799e3bb68a496d9bc1ef1ea85265409"></a><!-- doxytag: member="prob.sql_in::non_central_t_pdf" ref="a4799e3bb68a496d9bc1ef1ea85265409" args="(float8 x, float8 df, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_t_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>Noncentrality parameter \( \delta \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a noncentral Student's t-distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \delta \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01284">1284</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="af50865aba2ece2e23b2af461a02f7d12"></a><!-- doxytag: member="prob.sql_in::non_central_t_quantile" ref="af50865aba2ece2e23b2af461a02f7d12" args="(float8 p, float8 df, float8 ncp)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 non_central_t_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>ncp</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| <tr><td class="paramname">ncp</td><td>Noncentrality parameter \( \delta \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a noncentral Student's t-distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \delta \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01303">1303</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aebcd34ad7b1ca4b31d9699112c9a3b90"></a><!-- doxytag: member="prob.sql_in::normal_cdf" ref="aebcd34ad7b1ca4b31d9699112c9a3b90" args="(float8 x, float8 mean=0, float8 sd=1)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 normal_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em> = <code>0</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sd</em> = <code>1</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Mean \( \mu \) </td></tr> |
| <tr><td class="paramname">sd</td><td>Standard deviation \( \sigma > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( T \) is a normally distributed random variable with mean \( \mu \) and variance \( \sigma^2 \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01322">1322</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a63f555f36385d86e229cdca223e39567"></a><!-- doxytag: member="prob.sql_in::normal_pdf" ref="a63f555f36385d86e229cdca223e39567" args="(float8 x, float8 mean=0, float8 sd=1)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 normal_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em> = <code>0</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sd</em> = <code>1</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Mean \( \mu \) </td></tr> |
| <tr><td class="paramname">sd</td><td>Standard deviation \( \sigma > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a normally distributed random variable with mean \( \mu \) and variance \( \sigma^2 \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01360">1360</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a53d56b672fe4cd1277cb5eac5de5118f"></a><!-- doxytag: member="prob.sql_in::normal_quantile" ref="a53d56b672fe4cd1277cb5eac5de5118f" args="(float8 p, float8 mean=0, float8 sd=1)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 normal_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em> = <code>0</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>sd</em> = <code>1</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Mean \( \mu \) </td></tr> |
| <tr><td class="paramname">sd</td><td>Standard deviation \( \sigma > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a normally distributed random variable with mean \( \mu \) and variance \( \sigma^2 \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01398">1398</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aa1a42ebd68f20f65bc1784b427721b5d"></a><!-- doxytag: member="prob.sql_in::pareto_cdf" ref="aa1a42ebd68f20f65bc1784b427721b5d" args="(float8 x, float8 scale, float8 shape)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 pareto_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( \alpha > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a Pareto-distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01437">1437</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a22c56a6e48bc442435b13afac2a1eb37"></a><!-- doxytag: member="prob.sql_in::pareto_pdf" ref="a22c56a6e48bc442435b13afac2a1eb37" args="(float8 x, float8 scale, float8 shape)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 pareto_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( \alpha > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a Pareto-distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01456">1456</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a77779e2b5fa951189ccba6806c503c4d"></a><!-- doxytag: member="prob.sql_in::pareto_quantile" ref="a77779e2b5fa951189ccba6806c503c4d" args="(float8 p, float8 scale, float8 shape)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 pareto_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( \alpha > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Pareto-distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01475">1475</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ae0b4313d9fe730d6efb3f7c44206f345"></a><!-- doxytag: member="prob.sql_in::poisson_cdf" ref="ae0b4313d9fe730d6efb3f7c44206f345" args="(float8 x, float8 mean)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 poisson_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Average occurrence rate \( \lambda > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a Poisson distributed random variable with mean \( \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01493">1493</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a82f1edc27261021c73cd080ff2677a9f"></a><!-- doxytag: member="prob.sql_in::poisson_pmf" ref="a82f1edc27261021c73cd080ff2677a9f" args="(int4 x, float8 mean)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 poisson_pmf </td> |
| <td>(</td> |
| <td class="paramtype">int4 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Average occurrence rate \( \lambda > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability mass function of a Poisson distributed random variable with mean \( \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01509">1509</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a032d26db18b2ee1034085f5521939c61"></a><!-- doxytag: member="prob.sql_in::poisson_quantile" ref="a032d26db18b2ee1034085f5521939c61" args="(float8 p, float8 mean)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 poisson_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mean</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">mean</td><td>Average occurrence rate \( \lambda > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>If \( p < 0.5 \) the maximum \( x \) such that \( p \geq \Pr[X \leq x] \). If \( p \geq 0.5 \) the minimum \( x \) such that \( p \leq \Pr[X \leq x] \). Here, \( X \) is a Poisson distributed random variable with mean \( \lambda \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01527">1527</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aab0ddb8a5348cfa387d777043a3cb6d0"></a><!-- doxytag: member="prob.sql_in::rayleigh_cdf" ref="aab0ddb8a5348cfa387d777043a3cb6d0" args="(float8 x, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 rayleigh_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \sigma > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a Rayleigh-distributed random variable with parameter \( \sigma \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01544">1544</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a798541736d9255bdd5c0bd94924d47bc"></a><!-- doxytag: member="prob.sql_in::rayleigh_pdf" ref="a798541736d9255bdd5c0bd94924d47bc" args="(float8 x, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 rayleigh_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \sigma > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a Rayleigh-distributed random variable with parameter \( \sigma \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01560">1560</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="acd6757acab1683c735e2b57901494336"></a><!-- doxytag: member="prob.sql_in::rayleigh_quantile" ref="acd6757acab1683c735e2b57901494336" args="(float8 p, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 rayleigh_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \sigma > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Rayleigh-distributed random variable with parameter \( \sigma \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01576">1576</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a5322531131074c23a2dbf067ee504ef7"></a><!-- doxytag: member="prob.sql_in::students_t_cdf" ref="a5322531131074c23a2dbf067ee504ef7" args="(float8 x, float8 df)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 students_t_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a Student's t-distributed random variable with \( \nu \) degrees of freedom </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01593">1593</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a8815c21670fff9d31946553a84b845b1"></a><!-- doxytag: member="prob.sql_in::students_t_pdf" ref="a8815c21670fff9d31946553a84b845b1" args="(float8 x, float8 df)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 students_t_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a Stundent's t-distributed random variable with \( \nu \) degrees of freedom </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01610">1610</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a7d64add02af21a95d73502b2dd466a75"></a><!-- doxytag: member="prob.sql_in::students_t_quantile" ref="a7d64add02af21a95d73502b2dd466a75" args="(float8 p, float8 df)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 students_t_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>df</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">df</td><td>Degrees of freedom \( \nu > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Student's t-distributed random variable with \( \nu \) degrees of freedom </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01627">1627</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="abf9c7d870bcfe68cacaa421749bbdf35"></a><!-- doxytag: member="prob.sql_in::triangular_cdf" ref="abf9c7d870bcfe68cacaa421749bbdf35" args="(float8 x, float8 lower, float8 mode, float8 upper)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 triangular_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>lower</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mode</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>upper</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">lower</td><td>Lower bound \( a \) </td></tr> |
| <tr><td class="paramname">mode</td><td>Mode \( c \geq a \) </td></tr> |
| <tr><td class="paramname">upper</td><td>Upper bound \( b \geq c \), where \( b > a \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a triangular distributed random variable with parameters \( a, b, c \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01646">1646</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a0c511b9748b2f7a21fe56aaf5f66d188"></a><!-- doxytag: member="prob.sql_in::triangular_pdf" ref="a0c511b9748b2f7a21fe56aaf5f66d188" args="(float8 x, float8 lower, float8 mode, float8 upper)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 triangular_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>lower</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mode</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>upper</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">lower</td><td>Lower bound \( a \) </td></tr> |
| <tr><td class="paramname">mode</td><td>Mode \( c \geq a \) </td></tr> |
| <tr><td class="paramname">upper</td><td>Upper bound \( b \geq c \), where \( b > a \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a triangular distributed random variable with parameters \( a, b, c \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01666">1666</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a4777540ab1b003ff92d484c4bc26af27"></a><!-- doxytag: member="prob.sql_in::triangular_quantile" ref="a4777540ab1b003ff92d484c4bc26af27" args="(float8 p, float8 lower, float8 mode, float8 upper)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 triangular_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>lower</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>mode</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>upper</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">lower</td><td>Lower bound \( a \) </td></tr> |
| <tr><td class="paramname">mode</td><td>Mode \( c \geq a \) </td></tr> |
| <tr><td class="paramname">upper</td><td>Upper bound \( b \geq c \), where \( b > a \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a trianbular distributed random variable with parameters \( a, b, c \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01686">1686</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aa3a05f4f2e0ef9eb65e828261ecfbed9"></a><!-- doxytag: member="prob.sql_in::uniform_cdf" ref="aa3a05f4f2e0ef9eb65e828261ecfbed9" args="(float8 x, float8 lower, float8 upper)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 uniform_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>lower</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>upper</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">lower</td><td>Lower bound \( a \) </td></tr> |
| <tr><td class="paramname">upper</td><td>Upper bound \( b \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a uniform distributed random variable with support \( [a, b] \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01706">1706</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ab90fa34d90a9c75747a34c3f210df239"></a><!-- doxytag: member="prob.sql_in::uniform_pdf" ref="ab90fa34d90a9c75747a34c3f210df239" args="(float8 x, float8 lower, float8 upper)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 uniform_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>lower</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>upper</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">lower</td><td>Lower bound \( a \) </td></tr> |
| <tr><td class="paramname">upper</td><td>Upper bound \( b \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a uniform distributed random variable with support \( [a, b] \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01724">1724</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a629587a0fdefb588d28b15517ae5cc04"></a><!-- doxytag: member="prob.sql_in::uniform_quantile" ref="a629587a0fdefb588d28b15517ae5cc04" args="(float8 p, float8 lower, float8 upper)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 uniform_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>lower</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>upper</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">lower</td><td>Lower bound \( a \) </td></tr> |
| <tr><td class="paramname">upper</td><td>Upper bound \( b \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a uniform distributed random variable with support \( [a, b] \) </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01742">1742</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a50e4a1883588cd7a4c1ff1017399e4af"></a><!-- doxytag: member="prob.sql_in::weibull_cdf" ref="a50e4a1883588cd7a4c1ff1017399e4af" args="(float8 x, float8 shape, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 weibull_cdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( \Pr[X \leq x] \) where \( X \) is a weibull distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01762">1762</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a81a876ae2b8598f060dadb179b9324d2"></a><!-- doxytag: member="prob.sql_in::weibull_pdf" ref="a81a876ae2b8598f060dadb179b9324d2" args="(float8 x, float8 shape, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 weibull_pdf </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">x</td><td>Random variate \( x \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( f(x) \) where \( f \) is the probability density function of a weibull distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01781">1781</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aa544631ddeb7a5c06b995b4383c3b612"></a><!-- doxytag: member="prob.sql_in::weibull_quantile" ref="aa544631ddeb7a5c06b995b4383c3b612" args="(float8 p, float8 shape, float8 scale)" --> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 weibull_quantile </td> |
| <td>(</td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>p</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>shape</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>scale</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| <dl><dt><b>Parameters:</b></dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">p</td><td>Probability \( p \in [0,1] \) </td></tr> |
| <tr><td class="paramname">shape</td><td>Shape \( \alpha > 0 \) </td></tr> |
| <tr><td class="paramname">scale</td><td>Scale \( \beta > 0 \) </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="return"><dt><b>Returns:</b></dt><dd>\( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a weibull distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively </dd></dl> |
| |
| <p>Definition at line <a class="el" href="prob_8sql__in_source.html#l01800">1800</a> of file <a class="el" href="prob_8sql__in_source.html">prob.sql_in</a>.</p> |
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