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| </pre><pre class="rust"><code><span class="comment">// Copyright 2021 Developers of the Rand project. |
| // |
| // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or |
| // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license |
| // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your |
| // option. This file may not be copied, modified, or distributed |
| // except according to those terms. |
| |
| </span><span class="doccomment">//! The Fréchet distribution. |
| |
| </span><span class="kw">use crate</span>::{Distribution, OpenClosed01}; |
| <span class="kw">use </span>core::fmt; |
| <span class="kw">use </span>num_traits::Float; |
| <span class="kw">use </span>rand::Rng; |
| |
| <span class="doccomment">/// Samples floating-point numbers according to the Fréchet distribution |
| /// |
| /// This distribution has density function: |
| /// `f(x) = [(x - μ) / σ]^(-1 - α) exp[-(x - μ) / σ]^(-α) α / σ`, |
| /// where `μ` is the location parameter, `σ` the scale parameter, and `α` the shape parameter. |
| /// |
| /// # Example |
| /// ``` |
| /// use rand::prelude::*; |
| /// use rand_distr::Frechet; |
| /// |
| /// let val: f64 = thread_rng().sample(Frechet::new(0.0, 1.0, 1.0).unwrap()); |
| /// println!("{}", val); |
| /// ``` |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(serde::Serialize, serde::Deserialize))] |
| </span><span class="kw">pub struct </span>Frechet<F> |
| <span class="kw">where |
| </span>F: Float, |
| OpenClosed01: Distribution<F>, |
| { |
| location: F, |
| scale: F, |
| shape: F, |
| } |
| |
| <span class="doccomment">/// Error type returned from `Frechet::new`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| </span><span class="kw">pub enum </span>Error { |
| <span class="doccomment">/// location is infinite or NaN |
| </span>LocationNotFinite, |
| <span class="doccomment">/// scale is not finite positive number |
| </span>ScaleNotPositive, |
| <span class="doccomment">/// shape is not finite positive number |
| </span>ShapeNotPositive, |
| } |
| |
| <span class="kw">impl </span>fmt::Display <span class="kw">for </span>Error { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| f.write_str(<span class="kw">match </span><span class="self">self </span>{ |
| Error::LocationNotFinite => <span class="string">"location is not finite in Frechet distribution"</span>, |
| Error::ScaleNotPositive => <span class="string">"scale is not positive and finite in Frechet distribution"</span>, |
| Error::ShapeNotPositive => <span class="string">"shape is not positive and finite in Frechet distribution"</span>, |
| }) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| #[cfg_attr(doc_cfg, doc(cfg(feature = <span class="string">"std"</span>)))] |
| </span><span class="kw">impl </span>std::error::Error <span class="kw">for </span>Error {} |
| |
| <span class="kw">impl</span><F> Frechet<F> |
| <span class="kw">where |
| </span>F: Float, |
| OpenClosed01: Distribution<F>, |
| { |
| <span class="doccomment">/// Construct a new `Frechet` distribution with given `location`, `scale`, and `shape`. |
| </span><span class="kw">pub fn </span>new(location: F, scale: F, shape: F) -> <span class="prelude-ty">Result</span><Frechet<F>, Error> { |
| <span class="kw">if </span>scale <= F::zero() || scale.is_infinite() || scale.is_nan() { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::ScaleNotPositive); |
| } |
| <span class="kw">if </span>shape <= F::zero() || shape.is_infinite() || shape.is_nan() { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::ShapeNotPositive); |
| } |
| <span class="kw">if </span>location.is_infinite() || location.is_nan() { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::LocationNotFinite); |
| } |
| <span class="prelude-val">Ok</span>(Frechet { |
| location, |
| scale, |
| shape, |
| }) |
| } |
| } |
| |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>Frechet<F> |
| <span class="kw">where |
| </span>F: Float, |
| OpenClosed01: Distribution<F>, |
| { |
| <span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> F { |
| <span class="kw">let </span>x: F = rng.sample(OpenClosed01); |
| <span class="self">self</span>.location + <span class="self">self</span>.scale * (-x.ln()).powf(-<span class="self">self</span>.shape.recip()) |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use super</span>::<span class="kw-2">*</span>; |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_zero_scale() { |
| Frechet::new(<span class="number">0.0</span>, <span class="number">0.0</span>, <span class="number">1.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_infinite_scale() { |
| Frechet::new(<span class="number">0.0</span>, core::f64::INFINITY, <span class="number">1.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_nan_scale() { |
| Frechet::new(<span class="number">0.0</span>, core::f64::NAN, <span class="number">1.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_zero_shape() { |
| Frechet::new(<span class="number">0.0</span>, <span class="number">1.0</span>, <span class="number">0.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_infinite_shape() { |
| Frechet::new(<span class="number">0.0</span>, <span class="number">1.0</span>, core::f64::INFINITY).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_nan_shape() { |
| Frechet::new(<span class="number">0.0</span>, <span class="number">1.0</span>, core::f64::NAN).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_infinite_location() { |
| Frechet::new(core::f64::INFINITY, <span class="number">1.0</span>, <span class="number">1.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_nan_location() { |
| Frechet::new(core::f64::NAN, <span class="number">1.0</span>, <span class="number">1.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_sample_against_cdf() { |
| <span class="kw">fn </span>quantile_function(x: f64) -> f64 { |
| (-x.ln()).recip() |
| } |
| <span class="kw">let </span>location = <span class="number">0.0</span>; |
| <span class="kw">let </span>scale = <span class="number">1.0</span>; |
| <span class="kw">let </span>shape = <span class="number">1.0</span>; |
| <span class="kw">let </span>iterations = <span class="number">100_000</span>; |
| <span class="kw">let </span>increment = <span class="number">1.0 </span>/ iterations <span class="kw">as </span>f64; |
| <span class="kw">let </span>probabilities = [<span class="number">0.1</span>, <span class="number">0.2</span>, <span class="number">0.3</span>, <span class="number">0.4</span>, <span class="number">0.5</span>, <span class="number">0.6</span>, <span class="number">0.7</span>, <span class="number">0.8</span>, <span class="number">0.9</span>]; |
| <span class="kw">let </span><span class="kw-2">mut </span>quantiles = [<span class="number">0.0</span>; <span class="number">9</span>]; |
| <span class="kw">for </span>(i, p) <span class="kw">in </span>probabilities.iter().enumerate() { |
| quantiles[i] = quantile_function(<span class="kw-2">*</span>p); |
| } |
| <span class="kw">let </span><span class="kw-2">mut </span>proportions = [<span class="number">0.0</span>; <span class="number">9</span>]; |
| <span class="kw">let </span>d = Frechet::new(location, scale, shape).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">1</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..iterations { |
| <span class="kw">let </span>replicate = d.sample(<span class="kw-2">&mut </span>rng); |
| <span class="kw">for </span>(i, q) <span class="kw">in </span>quantiles.iter().enumerate() { |
| <span class="kw">if </span>replicate < <span class="kw-2">*</span>q { |
| proportions[i] += increment; |
| } |
| } |
| } |
| <span class="macro">assert!</span>(proportions |
| .iter() |
| .zip(<span class="kw-2">&</span>probabilities) |
| .all(|(p_hat, p)| (p_hat - p).abs() < <span class="number">0.003</span>)) |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="rand_distr" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |