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</pre><pre class="rust ">
<span class="comment">// Copyright 2013 The Rust Project Developers. See the COPYRIGHT</span>
<span class="comment">// file at the top-level directory of this distribution and at</span>
<span class="comment">// http://rust-lang.org/COPYRIGHT.</span>
<span class="comment">//</span>
<span class="comment">// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or</span>
<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license</span>
<span class="comment">// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your</span>
<span class="comment">// option. This file may not be copied, modified, or distributed</span>
<span class="comment">// except according to those terms.</span>
<span class="comment">//</span>
<span class="comment">// ignore-lexer-test FIXME #15679</span>
<span class="doccomment">//! The Gamma and derived distributions.</span>
<span class="kw">use</span> <span class="self">self</span>::<span class="ident">GammaRepr</span>::<span class="kw-2">*</span>;
<span class="kw">use</span> <span class="self">self</span>::<span class="ident">ChiSquaredRepr</span>::<span class="kw-2">*</span>;
<span class="kw">use</span> {<span class="ident">Rng</span>, <span class="ident">Open01</span>};
<span class="kw">use</span> <span class="kw">super</span>::<span class="ident">normal</span>::<span class="ident">StandardNormal</span>;
<span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">IndependentSample</span>, <span class="ident">Sample</span>, <span class="ident">Exp</span>};
<span class="doccomment">/// The Gamma distribution `Gamma(shape, scale)` distribution.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The density function of this distribution is</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```text</span>
<span class="doccomment">/// f(x) = x^(k - 1) * exp(-x / θ) / (Γ(k) * θ^k)</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">///</span>
<span class="doccomment">/// where `Γ` is the Gamma function, `k` is the shape and `θ` is the</span>
<span class="doccomment">/// scale and both `k` and `θ` are strictly positive.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The algorithm used is that described by Marsaglia & Tsang 2000[1],</span>
<span class="doccomment">/// falling back to directly sampling from an Exponential for `shape</span>
<span class="doccomment">/// == 1`, and using the boosting technique described in [1] for</span>
<span class="doccomment">/// `shape < 1`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Example</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```rust</span>
<span class="doccomment">/// use rand::distributions::{IndependentSample, Gamma};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let gamma = Gamma::new(2.0, 5.0);</span>
<span class="doccomment">/// let v = gamma.ind_sample(&mut rand::thread_rng());</span>
<span class="doccomment">/// println!("{} is from a Gamma(2, 5) distribution", v);</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">///</span>
<span class="doccomment">/// [1]: George Marsaglia and Wai Wan Tsang. 2000. "A Simple Method</span>
<span class="doccomment">/// for Generating Gamma Variables" *ACM Trans. Math. Softw.* 26, 3</span>
<span class="doccomment">/// (September 2000),</span>
<span class="doccomment">/// 363-372. DOI:[10.1145/358407.358414](http://doi.acm.org/10.1145/358407.358414)</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>)]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Gamma</span> {
<span class="ident">repr</span>: <span class="ident">GammaRepr</span>,
}
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>)]</span>
<span class="kw">enum</span> <span class="ident">GammaRepr</span> {
<span class="ident">Large</span>(<span class="ident">GammaLargeShape</span>),
<span class="ident">One</span>(<span class="ident">Exp</span>),
<span class="ident">Small</span>(<span class="ident">GammaSmallShape</span>)
}
<span class="comment">// These two helpers could be made public, but saving the</span>
<span class="comment">// match-on-Gamma-enum branch from using them directly (e.g. if one</span>
<span class="comment">// knows that the shape is always > 1) doesn't appear to be much</span>
<span class="comment">// faster.</span>
<span class="doccomment">/// Gamma distribution where the shape parameter is less than 1.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Note, samples from this require a compulsory floating-point `pow`</span>
<span class="doccomment">/// call, which makes it significantly slower than sampling from a</span>
<span class="doccomment">/// gamma distribution where the shape parameter is greater than or</span>
<span class="doccomment">/// equal to 1.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// See `Gamma` for sampling from a Gamma distribution with general</span>
<span class="doccomment">/// shape parameters.</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>)]</span>
<span class="kw">struct</span> <span class="ident">GammaSmallShape</span> {
<span class="ident">inv_shape</span>: <span class="ident">f64</span>,
<span class="ident">large_shape</span>: <span class="ident">GammaLargeShape</span>
}
<span class="doccomment">/// Gamma distribution where the shape parameter is larger than 1.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// See `Gamma` for sampling from a Gamma distribution with general</span>
<span class="doccomment">/// shape parameters.</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>)]</span>
<span class="kw">struct</span> <span class="ident">GammaLargeShape</span> {
<span class="ident">scale</span>: <span class="ident">f64</span>,
<span class="ident">c</span>: <span class="ident">f64</span>,
<span class="ident">d</span>: <span class="ident">f64</span>
}
<span class="kw">impl</span> <span class="ident">Gamma</span> {
<span class="doccomment">/// Construct an object representing the `Gamma(shape, scale)`</span>
<span class="doccomment">/// distribution.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Panics if `shape <= 0` or `scale <= 0`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">shape</span>: <span class="ident">f64</span>, <span class="ident">scale</span>: <span class="ident">f64</span>) <span class="op">-></span> <span class="ident">Gamma</span> {
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">shape</span> <span class="op">></span> <span class="number">0.0</span>, <span class="string">"Gamma::new called with shape <= 0"</span>);
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">scale</span> <span class="op">></span> <span class="number">0.0</span>, <span class="string">"Gamma::new called with scale <= 0"</span>);
<span class="kw">let</span> <span class="ident">repr</span> <span class="op">=</span> <span class="kw">match</span> <span class="ident">shape</span> {
<span class="number">1.0</span> <span class="op">=></span> <span class="ident">One</span>(<span class="ident">Exp</span>::<span class="ident">new</span>(<span class="number">1.0</span> <span class="op">/</span> <span class="ident">scale</span>)),
<span class="number">0.0</span> ... <span class="number">1.0</span> <span class="op">=></span> <span class="ident">Small</span>(<span class="ident">GammaSmallShape</span>::<span class="ident">new_raw</span>(<span class="ident">shape</span>, <span class="ident">scale</span>)),
_ <span class="op">=></span> <span class="ident">Large</span>(<span class="ident">GammaLargeShape</span>::<span class="ident">new_raw</span>(<span class="ident">shape</span>, <span class="ident">scale</span>))
};
<span class="ident">Gamma</span> { <span class="ident">repr</span>: <span class="ident">repr</span> }
}
}
<span class="kw">impl</span> <span class="ident">GammaSmallShape</span> {
<span class="kw">fn</span> <span class="ident">new_raw</span>(<span class="ident">shape</span>: <span class="ident">f64</span>, <span class="ident">scale</span>: <span class="ident">f64</span>) <span class="op">-></span> <span class="ident">GammaSmallShape</span> {
<span class="ident">GammaSmallShape</span> {
<span class="ident">inv_shape</span>: <span class="number">1.</span> <span class="op">/</span> <span class="ident">shape</span>,
<span class="ident">large_shape</span>: <span class="ident">GammaLargeShape</span>::<span class="ident">new_raw</span>(<span class="ident">shape</span> <span class="op">+</span> <span class="number">1.0</span>, <span class="ident">scale</span>)
}
}
}
<span class="kw">impl</span> <span class="ident">GammaLargeShape</span> {
<span class="kw">fn</span> <span class="ident">new_raw</span>(<span class="ident">shape</span>: <span class="ident">f64</span>, <span class="ident">scale</span>: <span class="ident">f64</span>) <span class="op">-></span> <span class="ident">GammaLargeShape</span> {
<span class="kw">let</span> <span class="ident">d</span> <span class="op">=</span> <span class="ident">shape</span> <span class="op">-</span> <span class="number">1.</span> <span class="op">/</span> <span class="number">3.</span>;
<span class="ident">GammaLargeShape</span> {
<span class="ident">scale</span>: <span class="ident">scale</span>,
<span class="ident">c</span>: <span class="number">1.</span> <span class="op">/</span> (<span class="number">9.</span> <span class="op">*</span> <span class="ident">d</span>).<span class="ident">sqrt</span>(),
<span class="ident">d</span>: <span class="ident">d</span>
}
}
}
<span class="kw">impl</span> <span class="ident">Sample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Gamma</span> {
<span class="kw">fn</span> <span class="ident">sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> { <span class="self">self</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>) }
}
<span class="kw">impl</span> <span class="ident">Sample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">GammaSmallShape</span> {
<span class="kw">fn</span> <span class="ident">sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> { <span class="self">self</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>) }
}
<span class="kw">impl</span> <span class="ident">Sample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">GammaLargeShape</span> {
<span class="kw">fn</span> <span class="ident">sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> { <span class="self">self</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>) }
}
<span class="kw">impl</span> <span class="ident">IndependentSample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Gamma</span> {
<span class="kw">fn</span> <span class="ident">ind_sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> {
<span class="kw">match</span> <span class="self">self</span>.<span class="ident">repr</span> {
<span class="ident">Small</span>(<span class="kw-2">ref</span> <span class="ident">g</span>) <span class="op">=></span> <span class="ident">g</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>),
<span class="ident">One</span>(<span class="kw-2">ref</span> <span class="ident">g</span>) <span class="op">=></span> <span class="ident">g</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>),
<span class="ident">Large</span>(<span class="kw-2">ref</span> <span class="ident">g</span>) <span class="op">=></span> <span class="ident">g</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>),
}
}
}
<span class="kw">impl</span> <span class="ident">IndependentSample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">GammaSmallShape</span> {
<span class="kw">fn</span> <span class="ident">ind_sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> {
<span class="kw">let</span> <span class="ident">Open01</span>(<span class="ident">u</span>) <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">gen</span>::<span class="op"><</span><span class="ident">Open01</span><span class="op"><</span><span class="ident">f64</span><span class="op">>></span>();
<span class="self">self</span>.<span class="ident">large_shape</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>) <span class="op">*</span> <span class="ident">u</span>.<span class="ident">powf</span>(<span class="self">self</span>.<span class="ident">inv_shape</span>)
}
}
<span class="kw">impl</span> <span class="ident">IndependentSample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">GammaLargeShape</span> {
<span class="kw">fn</span> <span class="ident">ind_sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> {
<span class="kw">loop</span> {
<span class="kw">let</span> <span class="ident">StandardNormal</span>(<span class="ident">x</span>) <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">gen</span>::<span class="op"><</span><span class="ident">StandardNormal</span><span class="op">></span>();
<span class="kw">let</span> <span class="ident">v_cbrt</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">c</span> <span class="op">*</span> <span class="ident">x</span>;
<span class="kw">if</span> <span class="ident">v_cbrt</span> <span class="op"><=</span> <span class="number">0.0</span> { <span class="comment">// a^3 <= 0 iff a <= 0</span>
<span class="kw">continue</span>
}
<span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">v_cbrt</span> <span class="op">*</span> <span class="ident">v_cbrt</span> <span class="op">*</span> <span class="ident">v_cbrt</span>;
<span class="kw">let</span> <span class="ident">Open01</span>(<span class="ident">u</span>) <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">gen</span>::<span class="op"><</span><span class="ident">Open01</span><span class="op"><</span><span class="ident">f64</span><span class="op">>></span>();
<span class="kw">let</span> <span class="ident">x_sqr</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>;
<span class="kw">if</span> <span class="ident">u</span> <span class="op"><</span> <span class="number">1.0</span> <span class="op">-</span> <span class="number">0.0331</span> <span class="op">*</span> <span class="ident">x_sqr</span> <span class="op">*</span> <span class="ident">x_sqr</span> <span class="op">||</span>
<span class="ident">u</span>.<span class="ident">ln</span>() <span class="op"><</span> <span class="number">0.5</span> <span class="op">*</span> <span class="ident">x_sqr</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">d</span> <span class="op">*</span> (<span class="number">1.0</span> <span class="op">-</span> <span class="ident">v</span> <span class="op">+</span> <span class="ident">v</span>.<span class="ident">ln</span>()) {
<span class="kw">return</span> <span class="self">self</span>.<span class="ident">d</span> <span class="op">*</span> <span class="ident">v</span> <span class="op">*</span> <span class="self">self</span>.<span class="ident">scale</span>
}
}
}
}
<span class="doccomment">/// The chi-squared distribution `χ²(k)`, where `k` is the degrees of</span>
<span class="doccomment">/// freedom.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// For `k > 0` integral, this distribution is the sum of the squares</span>
<span class="doccomment">/// of `k` independent standard normal random variables. For other</span>
<span class="doccomment">/// `k`, this uses the equivalent characterisation `χ²(k) = Gamma(k/2,</span>
<span class="doccomment">/// 2)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Example</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```rust</span>
<span class="doccomment">/// use rand::distributions::{ChiSquared, IndependentSample};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let chi = ChiSquared::new(11.0);</span>
<span class="doccomment">/// let v = chi.ind_sample(&mut rand::thread_rng());</span>
<span class="doccomment">/// println!("{} is from a χ²(11) distribution", v)</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>)]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">ChiSquared</span> {
<span class="ident">repr</span>: <span class="ident">ChiSquaredRepr</span>,
}
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>)]</span>
<span class="kw">enum</span> <span class="ident">ChiSquaredRepr</span> {
<span class="comment">// k == 1, Gamma(alpha, ..) is particularly slow for alpha < 1,</span>
<span class="comment">// e.g. when alpha = 1/2 as it would be for this case, so special-</span>
<span class="comment">// casing and using the definition of N(0,1)^2 is faster.</span>
<span class="ident">DoFExactlyOne</span>,
<span class="ident">DoFAnythingElse</span>(<span class="ident">Gamma</span>),
}
<span class="kw">impl</span> <span class="ident">ChiSquared</span> {
<span class="doccomment">/// Create a new chi-squared distribution with degrees-of-freedom</span>
<span class="doccomment">/// `k`. Panics if `k < 0`.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">k</span>: <span class="ident">f64</span>) <span class="op">-></span> <span class="ident">ChiSquared</span> {
<span class="kw">let</span> <span class="ident">repr</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">k</span> <span class="op">==</span> <span class="number">1.0</span> {
<span class="ident">DoFExactlyOne</span>
} <span class="kw">else</span> {
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">k</span> <span class="op">></span> <span class="number">0.0</span>, <span class="string">"ChiSquared::new called with `k` < 0"</span>);
<span class="ident">DoFAnythingElse</span>(<span class="ident">Gamma</span>::<span class="ident">new</span>(<span class="number">0.5</span> <span class="op">*</span> <span class="ident">k</span>, <span class="number">2.0</span>))
};
<span class="ident">ChiSquared</span> { <span class="ident">repr</span>: <span class="ident">repr</span> }
}
}
<span class="kw">impl</span> <span class="ident">Sample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">ChiSquared</span> {
<span class="kw">fn</span> <span class="ident">sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> { <span class="self">self</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>) }
}
<span class="kw">impl</span> <span class="ident">IndependentSample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">ChiSquared</span> {
<span class="kw">fn</span> <span class="ident">ind_sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> {
<span class="kw">match</span> <span class="self">self</span>.<span class="ident">repr</span> {
<span class="ident">DoFExactlyOne</span> <span class="op">=></span> {
<span class="comment">// k == 1 => N(0,1)^2</span>
<span class="kw">let</span> <span class="ident">StandardNormal</span>(<span class="ident">norm</span>) <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">gen</span>::<span class="op"><</span><span class="ident">StandardNormal</span><span class="op">></span>();
<span class="ident">norm</span> <span class="op">*</span> <span class="ident">norm</span>
}
<span class="ident">DoFAnythingElse</span>(<span class="kw-2">ref</span> <span class="ident">g</span>) <span class="op">=></span> <span class="ident">g</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>)
}
}
}
<span class="doccomment">/// The Fisher F distribution `F(m, n)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This distribution is equivalent to the ratio of two normalised</span>
<span class="doccomment">/// chi-squared distributions, that is, `F(m,n) = (χ²(m)/m) /</span>
<span class="doccomment">/// (χ²(n)/n)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Example</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```rust</span>
<span class="doccomment">/// use rand::distributions::{FisherF, IndependentSample};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = FisherF::new(2.0, 32.0);</span>
<span class="doccomment">/// let v = f.ind_sample(&mut rand::thread_rng());</span>
<span class="doccomment">/// println!("{} is from an F(2, 32) distribution", v)</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>)]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">FisherF</span> {
<span class="ident">numer</span>: <span class="ident">ChiSquared</span>,
<span class="ident">denom</span>: <span class="ident">ChiSquared</span>,
<span class="comment">// denom_dof / numer_dof so that this can just be a straight</span>
<span class="comment">// multiplication, rather than a division.</span>
<span class="ident">dof_ratio</span>: <span class="ident">f64</span>,
}
<span class="kw">impl</span> <span class="ident">FisherF</span> {
<span class="doccomment">/// Create a new `FisherF` distribution, with the given</span>
<span class="doccomment">/// parameter. Panics if either `m` or `n` are not positive.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">m</span>: <span class="ident">f64</span>, <span class="ident">n</span>: <span class="ident">f64</span>) <span class="op">-></span> <span class="ident">FisherF</span> {
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">m</span> <span class="op">></span> <span class="number">0.0</span>, <span class="string">"FisherF::new called with `m < 0`"</span>);
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">n</span> <span class="op">></span> <span class="number">0.0</span>, <span class="string">"FisherF::new called with `n < 0`"</span>);
<span class="ident">FisherF</span> {
<span class="ident">numer</span>: <span class="ident">ChiSquared</span>::<span class="ident">new</span>(<span class="ident">m</span>),
<span class="ident">denom</span>: <span class="ident">ChiSquared</span>::<span class="ident">new</span>(<span class="ident">n</span>),
<span class="ident">dof_ratio</span>: <span class="ident">n</span> <span class="op">/</span> <span class="ident">m</span>
}
}
}
<span class="kw">impl</span> <span class="ident">Sample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">FisherF</span> {
<span class="kw">fn</span> <span class="ident">sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> { <span class="self">self</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>) }
}
<span class="kw">impl</span> <span class="ident">IndependentSample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">FisherF</span> {
<span class="kw">fn</span> <span class="ident">ind_sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> {
<span class="self">self</span>.<span class="ident">numer</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>) <span class="op">/</span> <span class="self">self</span>.<span class="ident">denom</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>) <span class="op">*</span> <span class="self">self</span>.<span class="ident">dof_ratio</span>
}
}
<span class="doccomment">/// The Student t distribution, `t(nu)`, where `nu` is the degrees of</span>
<span class="doccomment">/// freedom.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Example</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```rust</span>
<span class="doccomment">/// use rand::distributions::{StudentT, IndependentSample};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let t = StudentT::new(11.0);</span>
<span class="doccomment">/// let v = t.ind_sample(&mut rand::thread_rng());</span>
<span class="doccomment">/// println!("{} is from a t(11) distribution", v)</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>)]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">StudentT</span> {
<span class="ident">chi</span>: <span class="ident">ChiSquared</span>,
<span class="ident">dof</span>: <span class="ident">f64</span>
}
<span class="kw">impl</span> <span class="ident">StudentT</span> {
<span class="doccomment">/// Create a new Student t distribution with `n` degrees of</span>
<span class="doccomment">/// freedom. Panics if `n <= 0`.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">n</span>: <span class="ident">f64</span>) <span class="op">-></span> <span class="ident">StudentT</span> {
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">n</span> <span class="op">></span> <span class="number">0.0</span>, <span class="string">"StudentT::new called with `n <= 0`"</span>);
<span class="ident">StudentT</span> {
<span class="ident">chi</span>: <span class="ident">ChiSquared</span>::<span class="ident">new</span>(<span class="ident">n</span>),
<span class="ident">dof</span>: <span class="ident">n</span>
}
}
}
<span class="kw">impl</span> <span class="ident">Sample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">StudentT</span> {
<span class="kw">fn</span> <span class="ident">sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> { <span class="self">self</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>) }
}
<span class="kw">impl</span> <span class="ident">IndependentSample</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">StudentT</span> {
<span class="kw">fn</span> <span class="ident">ind_sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-></span> <span class="ident">f64</span> {
<span class="kw">let</span> <span class="ident">StandardNormal</span>(<span class="ident">norm</span>) <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">gen</span>::<span class="op"><</span><span class="ident">StandardNormal</span><span class="op">></span>();
<span class="ident">norm</span> <span class="op">*</span> (<span class="self">self</span>.<span class="ident">dof</span> <span class="op">/</span> <span class="self">self</span>.<span class="ident">chi</span>.<span class="ident">ind_sample</span>(<span class="ident">rng</span>)).<span class="ident">sqrt</span>()
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">mod</span> <span class="ident">test</span> {
<span class="kw">use</span> <span class="ident">distributions</span>::{<span class="ident">Sample</span>, <span class="ident">IndependentSample</span>};
<span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">ChiSquared</span>, <span class="ident">StudentT</span>, <span class="ident">FisherF</span>};
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_chi_squared_one</span>() {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">chi</span> <span class="op">=</span> <span class="ident">ChiSquared</span>::<span class="ident">new</span>(<span class="number">1.0</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> ::<span class="ident">test</span>::<span class="ident">rng</span>();
<span class="kw">for</span> _ <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
<span class="ident">chi</span>.<span class="ident">sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
<span class="ident">chi</span>.<span class="ident">ind_sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_chi_squared_small</span>() {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">chi</span> <span class="op">=</span> <span class="ident">ChiSquared</span>::<span class="ident">new</span>(<span class="number">0.5</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> ::<span class="ident">test</span>::<span class="ident">rng</span>();
<span class="kw">for</span> _ <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
<span class="ident">chi</span>.<span class="ident">sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
<span class="ident">chi</span>.<span class="ident">ind_sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_chi_squared_large</span>() {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">chi</span> <span class="op">=</span> <span class="ident">ChiSquared</span>::<span class="ident">new</span>(<span class="number">30.0</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> ::<span class="ident">test</span>::<span class="ident">rng</span>();
<span class="kw">for</span> _ <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
<span class="ident">chi</span>.<span class="ident">sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
<span class="ident">chi</span>.<span class="ident">ind_sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">should_panic</span>]</span>
<span class="kw">fn</span> <span class="ident">test_chi_squared_invalid_dof</span>() {
<span class="ident">ChiSquared</span>::<span class="ident">new</span>(<span class="op">-</span><span class="number">1.0</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_f</span>() {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">f</span> <span class="op">=</span> <span class="ident">FisherF</span>::<span class="ident">new</span>(<span class="number">2.0</span>, <span class="number">32.0</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> ::<span class="ident">test</span>::<span class="ident">rng</span>();
<span class="kw">for</span> _ <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
<span class="ident">f</span>.<span class="ident">sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
<span class="ident">f</span>.<span class="ident">ind_sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_t</span>() {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">t</span> <span class="op">=</span> <span class="ident">StudentT</span>::<span class="ident">new</span>(<span class="number">11.0</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> ::<span class="ident">test</span>::<span class="ident">rng</span>();
<span class="kw">for</span> _ <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
<span class="ident">t</span>.<span class="ident">sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
<span class="ident">t</span>.<span class="ident">ind_sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
}
}
}
</pre>
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