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| <div class="subTitle">org.apache.mahout.math.jet.stat</div> |
| <h2 title="Class Probability" class="title">Class Probability</h2> |
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| <li>org.apache.mahout.math.jet.stat.Probability</li> |
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| <pre>public final class <span class="typeNameLabel">Probability</span> |
| extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre> |
| <div class="block">Partially deprecated until unit tests are in place. Until this time, this class/interface is unsupported.</div> |
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| <th class="colFirst" scope="col">Modifier and Type</th> |
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| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/jet/stat/Probability.html#beta-double-double-double-">beta</a></span>(double a, |
| double b, |
| double x)</code> |
| <div class="block">Returns the area from zero to <tt>x</tt> under the beta density function.</div> |
| </td> |
| </tr> |
| <tr id="i1" class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/jet/stat/Probability.html#gamma-double-double-double-">gamma</a></span>(double alpha, |
| double beta, |
| double x)</code> |
| <div class="block">Returns the integral from zero to <tt>x</tt> of the gamma probability density function.</div> |
| </td> |
| </tr> |
| <tr id="i2" class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/jet/stat/Probability.html#negativeBinomial-int-int-double-">negativeBinomial</a></span>(int k, |
| int n, |
| double p)</code> |
| <div class="block">Returns the sum of the terms <tt>0</tt> through <tt>k</tt> of the Negative Binomial Distribution.</div> |
| </td> |
| </tr> |
| <tr id="i3" class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/jet/stat/Probability.html#normal-double-">normal</a></span>(double a)</code> |
| <div class="block">Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to |
| <tt>x</tt> (assumes mean is zero, variance is one).</div> |
| </td> |
| </tr> |
| <tr id="i4" class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/jet/stat/Probability.html#normal-double-double-double-">normal</a></span>(double mean, |
| double variance, |
| double x)</code> |
| <div class="block">Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to |
| <tt>x</tt>.</div> |
| </td> |
| </tr> |
| <tr id="i5" class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/jet/stat/Probability.html#poisson-int-double-">poisson</a></span>(int k, |
| double mean)</code> |
| <div class="block">Returns the sum of the first <tt>k</tt> terms of the Poisson distribution.</div> |
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| <h4>beta</h4> |
| <pre>public static double beta(double a, |
| double b, |
| double x)</pre> |
| <div class="block">Returns the area from zero to <tt>x</tt> under the beta density function. |
| <pre> |
| x |
| - - |
| | (a+b) | | a-1 b-1 |
| P(x) = ---------- | t (1-t) dt |
| - - | | |
| | (a) | (b) - |
| 0 |
| </pre> |
| This function is identical to the incomplete beta integral function <tt>Gamma.incompleteBeta(a, b, x)</tt>. |
| |
| The complemented function is |
| |
| <tt>1 - P(1-x) = Gamma.incompleteBeta( b, a, x )</tt>;</div> |
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| <h4>gamma</h4> |
| <pre>public static double gamma(double alpha, |
| double beta, |
| double x)</pre> |
| <div class="block">Returns the integral from zero to <tt>x</tt> of the gamma probability density function. |
| <pre> |
| |
| alpha - x |
| beta | alpha-1 -beta t |
| y = --------- | t e dt |
| - | |
| | (alpha) - 0 |
| </pre> |
| The incomplete gamma integral is used, according to the relation |
| |
| <tt>y = Gamma.incompleteGamma( alpha, beta*x )</tt>. |
| |
| See http://en.wikipedia.org/wiki/Gamma_distribution#Probability_density_function</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>alpha</code> - the shape parameter of the gamma distribution.</dd> |
| <dd><code>beta</code> - the rate parameter of the gamma distribution.</dd> |
| <dd><code>x</code> - integration end point.</dd> |
| </dl> |
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| <h4>negativeBinomial</h4> |
| <pre>public static double negativeBinomial(int k, |
| int n, |
| double p)</pre> |
| <div class="block">Returns the sum of the terms <tt>0</tt> through <tt>k</tt> of the Negative Binomial Distribution. |
| <code>k |
| -- ( n+j-1 ) n j |
| > ( ) p (1-p) |
| -- ( j ) |
| j=0 |
| </code> |
| In a sequence of Bernoulli trials, this is the probability that <tt>k</tt> or fewer failures precede the |
| <tt>n</tt>-th success. <p> The terms are not computed individually; instead the incomplete beta integral is |
| employed, according to the formula <p> <tt>y = negativeBinomial( k, n, p ) = Gamma.incompleteBeta( n, k+1, p |
| )</tt>. |
| |
| All arguments must be positive,</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>k</code> - end term.</dd> |
| <dd><code>n</code> - the number of trials.</dd> |
| <dd><code>p</code> - the probability of success (must be in <tt>(0.0,1.0)</tt>).</dd> |
| </dl> |
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| <h4>normal</h4> |
| <pre>public static double normal(double a)</pre> |
| <div class="block">Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to |
| <tt>x</tt> (assumes mean is zero, variance is one). |
| <code>x |
| - |
| 1 | | 2 |
| normal(x) = --------- | exp( - t /2 ) dt |
| sqrt(2pi) | | |
| - |
| -inf. |
| |
| = ( 1 + erf(z) ) / 2 |
| = erfc(z) / 2 |
| </code> |
| where <tt>z = x/sqrt(2)</tt>. Computation is via the functions <tt>errorFunction</tt> and |
| <tt>errorFunctionComplement</tt>. |
| <p> |
| Computed using method 26.2.17 from Abramovitz and Stegun (see http://www.math.sfu.ca/~cbm/aands/page_932.htm |
| and http://en.wikipedia.org/wiki/Normal_distribution#Numerical_approximations_of_the_normal_cdf</div> |
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| <h4>normal</h4> |
| <pre>public static double normal(double mean, |
| double variance, |
| double x)</pre> |
| <div class="block">Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to |
| <tt>x</tt>. |
| <code>x |
| - |
| 1 | | 2 |
| normal(x) = --------- | exp( - (t-mean) / 2v ) dt |
| sqrt(2pi*v)| | |
| - |
| -inf. |
| |
| </code> |
| where <tt>v = variance</tt>. Computation is via the functions <tt>errorFunction</tt>.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>mean</code> - the mean of the normal distribution.</dd> |
| <dd><code>variance</code> - the variance of the normal distribution.</dd> |
| <dd><code>x</code> - the integration limit.</dd> |
| </dl> |
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| <h4>poisson</h4> |
| <pre>public static double poisson(int k, |
| double mean)</pre> |
| <div class="block">Returns the sum of the first <tt>k</tt> terms of the Poisson distribution. |
| <pre> |
| k j |
| -- -m m |
| > e -- |
| -- j! |
| j=0 |
| </pre> |
| The terms are not summed directly; instead the incomplete gamma integral is employed, according to the relation <p> |
| <tt>y = poisson( k, m ) = Gamma.incompleteGammaComplement( k+1, m )</tt>. |
| |
| The arguments must both be positive.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>k</code> - number of terms.</dd> |
| <dd><code>mean</code> - the mean of the poisson distribution.</dd> |
| </dl> |
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