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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 Skew Normal distribution. |
| |
| </span><span class="kw">use crate</span>::{Distribution, StandardNormal}; |
| <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">/// The [skew normal distribution] `SN(location, scale, shape)`. |
| /// |
| /// The skew normal distribution is a generalization of the |
| /// [`Normal`] distribution to allow for non-zero skewness. |
| /// |
| /// It has the density function, for `scale > 0`, |
| /// `f(x) = 2 / scale * phi((x - location) / scale) * Phi(alpha * (x - location) / scale)` |
| /// where `phi` and `Phi` are the density and distribution of a standard normal variable. |
| /// |
| /// # Example |
| /// |
| /// ``` |
| /// use rand_distr::{SkewNormal, Distribution}; |
| /// |
| /// // location 2, scale 3, shape 1 |
| /// let skew_normal = SkewNormal::new(2.0, 3.0, 1.0).unwrap(); |
| /// let v = skew_normal.sample(&mut rand::thread_rng()); |
| /// println!("{} is from a SN(2, 3, 1) distribution", v) |
| /// ``` |
| /// |
| /// # Implementation details |
| /// |
| /// We are using the algorithm from [A Method to Simulate the Skew Normal Distribution]. |
| /// |
| /// [skew normal distribution]: https://en.wikipedia.org/wiki/Skew_normal_distribution |
| /// [`Normal`]: struct.Normal.html |
| /// [A Method to Simulate the Skew Normal Distribution]: https://dx.doi.org/10.4236/am.2014.513201 |
| </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>SkewNormal<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| { |
| location: F, |
| scale: F, |
| shape: F, |
| } |
| |
| <span class="doccomment">/// Error type returned from `SkewNormal::new`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| </span><span class="kw">pub enum </span>Error { |
| <span class="doccomment">/// The scale parameter is not finite or it is less or equal to zero. |
| </span>ScaleTooSmall, |
| <span class="doccomment">/// The shape parameter is not finite. |
| </span>BadShape, |
| } |
| |
| <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::ScaleTooSmall => { |
| <span class="string">"scale parameter is either non-finite or it is less or equal to zero in skew normal distribution" |
| </span>} |
| Error::BadShape => <span class="string">"shape parameter is non-finite in skew normal 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> SkewNormal<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| { |
| <span class="doccomment">/// Construct, from location, scale and shape. |
| /// |
| /// Parameters: |
| /// |
| /// - location (unrestricted) |
| /// - scale (must be finite and larger than zero) |
| /// - shape (must be finite) |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>new(location: F, scale: F, shape: F) -> <span class="prelude-ty">Result</span><SkewNormal<F>, Error> { |
| <span class="kw">if </span>!scale.is_finite() || !(scale > F::zero()) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::ScaleTooSmall); |
| } |
| <span class="kw">if </span>!shape.is_finite() { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::BadShape); |
| } |
| <span class="prelude-val">Ok</span>(SkewNormal { |
| location, |
| scale, |
| shape, |
| }) |
| } |
| |
| <span class="doccomment">/// Returns the location of the distribution. |
| </span><span class="kw">pub fn </span>location(<span class="kw-2">&</span><span class="self">self</span>) -> F { |
| <span class="self">self</span>.location |
| } |
| |
| <span class="doccomment">/// Returns the scale of the distribution. |
| </span><span class="kw">pub fn </span>scale(<span class="kw-2">&</span><span class="self">self</span>) -> F { |
| <span class="self">self</span>.scale |
| } |
| |
| <span class="doccomment">/// Returns the shape of the distribution. |
| </span><span class="kw">pub fn </span>shape(<span class="kw-2">&</span><span class="self">self</span>) -> F { |
| <span class="self">self</span>.shape |
| } |
| } |
| |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>SkewNormal<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: 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>linear_map = |x: F| -> F { x * <span class="self">self</span>.scale + <span class="self">self</span>.location }; |
| <span class="kw">let </span>u_1: F = rng.sample(StandardNormal); |
| <span class="kw">if </span><span class="self">self</span>.shape == F::zero() { |
| linear_map(u_1) |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>u_2 = rng.sample(StandardNormal); |
| <span class="kw">let </span>(u, v) = (u_1.max(u_2), u_1.min(u_2)); |
| <span class="kw">if </span><span class="self">self</span>.shape == -F::one() { |
| linear_map(v) |
| } <span class="kw">else if </span><span class="self">self</span>.shape == F::one() { |
| linear_map(u) |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>normalized = ((F::one() + <span class="self">self</span>.shape) * u + (F::one() - <span class="self">self</span>.shape) * v) |
| / ((F::one() + <span class="self">self</span>.shape * <span class="self">self</span>.shape).sqrt() |
| * F::from(core::f64::consts::SQRT_2).unwrap()); |
| linear_map(normalized) |
| } |
| } |
| } |
| } |
| |
| <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="kw">fn </span>test_samples<F: Float + core::fmt::Debug, D: Distribution<F>>( |
| distr: D, zero: F, expected: <span class="kw-2">&</span>[F], |
| ) { |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">213</span>); |
| <span class="kw">let </span><span class="kw-2">mut </span>buf = [zero; <span class="number">4</span>]; |
| <span class="kw">for </span>x <span class="kw">in </span><span class="kw-2">&mut </span>buf { |
| <span class="kw-2">*</span>x = rng.sample(<span class="kw-2">&</span>distr); |
| } |
| <span class="macro">assert_eq!</span>(buf, expected); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>invalid_scale_nan() { |
| SkewNormal::new(<span class="number">0.0</span>, core::f64::NAN, <span class="number">0.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>invalid_scale_zero() { |
| SkewNormal::new(<span class="number">0.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>invalid_scale_negative() { |
| SkewNormal::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>invalid_scale_infinite() { |
| SkewNormal::new(<span class="number">0.0</span>, core::f64::INFINITY, <span class="number">0.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>invalid_shape_nan() { |
| SkewNormal::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>invalid_shape_infinite() { |
| SkewNormal::new(<span class="number">0.0</span>, <span class="number">1.0</span>, core::f64::INFINITY).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>valid_location_nan() { |
| SkewNormal::new(core::f64::NAN, <span class="number">1.0</span>, <span class="number">0.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>skew_normal_value_stability() { |
| test_samples( |
| SkewNormal::new(<span class="number">0.0</span>, <span class="number">1.0</span>, <span class="number">0.0</span>).unwrap(), |
| <span class="number">0f32</span>, |
| <span class="kw-2">&</span>[-<span class="number">0.11844189</span>, <span class="number">0.781378</span>, <span class="number">0.06563994</span>, -<span class="number">1.1932899</span>], |
| ); |
| test_samples( |
| SkewNormal::new(<span class="number">0.0</span>, <span class="number">1.0</span>, <span class="number">0.0</span>).unwrap(), |
| <span class="number">0f64</span>, |
| <span class="kw-2">&</span>[ |
| -<span class="number">0.11844188827977231</span>, |
| <span class="number">0.7813779637772346</span>, |
| <span class="number">0.06563993969580051</span>, |
| -<span class="number">1.1932899004186373</span>, |
| ], |
| ); |
| test_samples( |
| SkewNormal::new(core::f64::INFINITY, <span class="number">1.0</span>, <span class="number">0.0</span>).unwrap(), |
| <span class="number">0f64</span>, |
| <span class="kw-2">&</span>[ |
| core::f64::INFINITY, |
| core::f64::INFINITY, |
| core::f64::INFINITY, |
| core::f64::INFINITY, |
| ], |
| ); |
| test_samples( |
| SkewNormal::new(core::f64::NEG_INFINITY, <span class="number">1.0</span>, <span class="number">0.0</span>).unwrap(), |
| <span class="number">0f64</span>, |
| <span class="kw-2">&</span>[ |
| core::f64::NEG_INFINITY, |
| core::f64::NEG_INFINITY, |
| core::f64::NEG_INFINITY, |
| core::f64::NEG_INFINITY, |
| ], |
| ); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>skew_normal_value_location_nan() { |
| <span class="kw">let </span>skew_normal = SkewNormal::new(core::f64::NAN, <span class="number">1.0</span>, <span class="number">0.0</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">213</span>); |
| <span class="kw">let </span><span class="kw-2">mut </span>buf = [<span class="number">0.0</span>; <span class="number">4</span>]; |
| <span class="kw">for </span>x <span class="kw">in </span><span class="kw-2">&mut </span>buf { |
| <span class="kw-2">*</span>x = rng.sample(<span class="kw-2">&</span>skew_normal); |
| } |
| <span class="kw">for </span>value <span class="kw">in </span>buf.iter() { |
| <span class="macro">assert!</span>(value.is_nan()); |
| } |
| } |
| } |
| </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> |
