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feat: added complete implementation for stats/base/dists/halfnormal
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‎lib/node_modules/@stdlib/stats/base/dists/halfnormal/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Half-Normal
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> Half-normal distribution.
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<section class="usage">
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## Usage
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```javascript
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var halfnormal = require( '@stdlib/stats/base/dists/halfnormal' );
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```
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#### halfnormal
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Half-normal distribution.
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```javascript
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var dist = halfnormal;
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// returns {...}
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```
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The namespace contains the following distribution functions:
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<!-- <toc pattern="*+(cdf|pdf|mgf|quantile)*"> -->
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<div class="namespace-toc">
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- <span class="signature">[`cdf( x, sigma )`][@stdlib/stats/base/dists/halfnormal/cdf]</span><span class="delimiter">: </span><span class="description">half-normal distribution cumulative distribution function.</span>
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- <span class="signature">[`logcdf( x, sigma )`][@stdlib/stats/base/dists/halfnormal/logcdf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the cumulative distribution function (CDF) for a half-normal distribution.</span>
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- <span class="signature">[`logpdf( x, sigma )`][@stdlib/stats/base/dists/halfnormal/logpdf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the probability density function (PDF) for a half-normal distribution.</span>
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- <span class="signature">[`mgf( t, sigma )`][@stdlib/stats/base/dists/halfnormal/mgf]</span><span class="delimiter">: </span><span class="description">half-normal distribution moment-generating function (MGF).</span>
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- <span class="signature">[`pdf( x, sigma )`][@stdlib/stats/base/dists/halfnormal/pdf]</span><span class="delimiter">: </span><span class="description">half-normal distribution probability density function (PDF).</span>
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- <span class="signature">[`quantile( p, sigma )`][@stdlib/stats/base/dists/halfnormal/quantile]</span><span class="delimiter">: </span><span class="description">half-normal distribution quantile function.</span>
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</div>
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<!-- </toc> -->
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The namespace contains the following functions for calculating distribution properties:
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<!-- <toc pattern="*+(entropy|kurtosis|mean|median|mode|skewness|stdev|variance)*"> -->
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<div class="namespace-toc">
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- <span class="signature">[`entropy( sigma )`][@stdlib/stats/base/dists/halfnormal/entropy]</span><span class="delimiter">: </span><span class="description">half-normal distribution differential entropy.</span>
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- <span class="signature">[`kurtosis( sigma )`][@stdlib/stats/base/dists/halfnormal/kurtosis]</span><span class="delimiter">: </span><span class="description">half-normal distribution excess kurtosis.</span>
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- <span class="signature">[`mean( sigma )`][@stdlib/stats/base/dists/halfnormal/mean]</span><span class="delimiter">: </span><span class="description">half-normal distribution expected value.</span>
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- <span class="signature">[`median( sigma )`][@stdlib/stats/base/dists/halfnormal/median]</span><span class="delimiter">: </span><span class="description">half-normal distribution median.</span>
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- <span class="signature">[`mode( sigma )`][@stdlib/stats/base/dists/halfnormal/mode]</span><span class="delimiter">: </span><span class="description">half-normal distribution mode.</span>
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- <span class="signature">[`skewness( sigma )`][@stdlib/stats/base/dists/halfnormal/skewness]</span><span class="delimiter">: </span><span class="description">half-normal distribution skewness.</span>
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- <span class="signature">[`stdev( sigma )`][@stdlib/stats/base/dists/halfnormal/stdev]</span><span class="delimiter">: </span><span class="description">half-normal distribution standard deviation.</span>
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- <span class="signature">[`variance( sigma )`][@stdlib/stats/base/dists/halfnormal/variance]</span><span class="delimiter">: </span><span class="description">half-normal distribution variance.</span>
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</div>
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<!-- </toc> -->
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The namespace contains a constructor function for creating a [half-normal][halfnormal-distribution] distribution object.
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<!-- <toc pattern="*ctor*"> -->
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<div class="namespace-toc">
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- <span class="signature">[`HalfNormal( [sigma] )`][@stdlib/stats/base/dists/halfnormal/ctor]</span><span class="delimiter">: </span><span class="description">half-normal distribution constructor.</span>
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</div>
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<!-- </toc> -->
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```javascript
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var HalfNormal = require( '@stdlib/stats/base/dists/halfnormal' ).HalfNormal;
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var dist = new HalfNormal( 2.0 );
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var y = dist.pdf( 1.0 );
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// returns 0.3520653267642996
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var halfnormal = require( '@stdlib/stats/base/dists/halfnormal' );
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/*
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A quality control engineer is analyzing the absolute deviations of product measurements from their target specification.
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The absolute deviations follow a half-normal distribution with scale parameter σ (sigma) = 2.0 mm.
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We can model these absolute deviations using a half-normal distribution with σ = 2.0.
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*/
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var sigma = 2.0;
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var halfnormalDist = new halfnormal.HalfNormal( sigma );
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// Output the scale parameter:
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console.log( halfnormalDist.sigma );
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// => 2.0
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// Mean absolute deviation:
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console.log( halfnormalDist.mean );
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// => ~1.596
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// Median absolute deviation:
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console.log( halfnormalDist.median );
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// => ~1.349
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// Mode (most common deviation):
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console.log( halfnormalDist.mode );
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// => 0.0
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// Variance of absolute deviations:
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console.log( halfnormalDist.variance );
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// => 1.4535209105296745
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// Probability density function at 1.0 mm deviation:
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console.log( halfnormal.pdf( 1.0, sigma ) );
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// => 0.3520653267642996
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// Cumulative distribution function at 2.0 mm (portion of deviations ≤ 2.0 mm):
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console.log( halfnormal.cdf( 2.0, sigma ) );
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// => ~0.683
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// 90th percentile of absolute deviations:
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console.log( halfnormal.quantile( 0.9, sigma ) );
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// => 3.289707253902946
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// Moment-generating function value at 0.5:
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console.log( halfnormal.mgf( 0.5, sigma ) );
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// => 2.7742859576700094
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// Entropy (measure of uncertainty):
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console.log( halfnormal.entropy( sigma ) );
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// => 1.4189385332046727
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// Skewness (measure of asymmetry):
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console.log( halfnormal.skewness( sigma ) );
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// => ~0.995
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// Excess kurtosis (measure of tail heaviness):
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console.log( halfnormal.kurtosis( sigma ) );
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// => ~0.869
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var myquantile = halfnormal.quantile.factory( 2.0 );
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// 25th percentile:
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console.log( myquantile( 0.25 ) );
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// => 0.6372787279287504
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// 75th percentile:
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console.log( myquantile( 0.75 ) );
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// => 2.300698760752016
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var mylogpdf = halfnormal.logpdf.factory( 2.0 );
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// Logarithm of PDF at 1.0 mm:
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console.log( mylogpdf( 1.0 ) );
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// => -1.0439385332046727
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// Logarithm of PDF at 3.0 mm:
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console.log( mylogpdf( 3.0 ) );
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// => -2.0439385332046727
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[halfnormal-distribution]: https://en.wikipedia.org/wiki/Half-normal_distribution
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<!-- <toc-links> -->
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[@stdlib/stats/base/dists/halfnormal/ctor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/ctor
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[@stdlib/stats/base/dists/halfnormal/entropy]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/entropy
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[@stdlib/stats/base/dists/halfnormal/kurtosis]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/kurtosis
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[@stdlib/stats/base/dists/halfnormal/mean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/mean
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[@stdlib/stats/base/dists/halfnormal/median]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/median
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[@stdlib/stats/base/dists/halfnormal/mode]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/mode
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[@stdlib/stats/base/dists/halfnormal/skewness]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/skewness
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[@stdlib/stats/base/dists/halfnormal/stdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/stdev
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[@stdlib/stats/base/dists/halfnormal/variance]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/variance
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[@stdlib/stats/base/dists/halfnormal/cdf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/cdf
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[@stdlib/stats/base/dists/halfnormal/logcdf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/logcdf
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[@stdlib/stats/base/dists/halfnormal/logpdf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/logpdf
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[@stdlib/stats/base/dists/halfnormal/mgf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/mgf
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[@stdlib/stats/base/dists/halfnormal/pdf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/pdf
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[@stdlib/stats/base/dists/halfnormal/quantile]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/halfnormal/quantile
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<!-- </toc-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/dists/halfnormal/cdf/lib/factory.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var constantFunction = require( '@stdlib/utils/constant-function' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var sqrt = require( '@stdlib/math/base/special/sqrt' );
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var erf = require( '@stdlib/math/base/special/erf' );
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// MAIN //
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/**
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* Returns a function for evaluating the cumulative distribution function (CDF) for a half-normal distribution.
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*
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* @param {PositiveNumber} sigma - scale parameter
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* @returns {Function} function to evaluate the cumulative distribution function
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*
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* @example
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* var cdf = factory( 2.0 );
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* var y = cdf( 1.0 );
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* // returns 0.3829249225480262
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*
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* y = cdf( 0.0 );
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* // returns 0.0
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*/
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function factory( sigma ) {
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var denom;
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if (
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isnan( sigma ) ||
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sigma < 0.0
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) {
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return constantFunction( NaN );
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}
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if ( sigma === 0.0 ) {
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return cdf;
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}
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denom = sigma * sqrt( 2.0 );
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return cdf;
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/**
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* Evaluates the cumulative distribution function (CDF) for a half-normal distribution.
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*
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* @private
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* @param {number} x - input value
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* @returns {Probability} evaluated cumulative distribution function
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*
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* @example
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* var y = cdf( 2.0 );
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* // returns <number>
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*/
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function cdf( x ) {
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if ( isnan( x ) ) {
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return NaN;
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}
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if ( x < 0.0 ) {
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return 0.0;
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}
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if ( sigma === 0.0 ) {
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return ( x >= 0.0 ) ? 1.0 : 0.0;
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}
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return erf( x / denom );
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}
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}
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// EXPORTS //
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module.exports = factory;

‎lib/node_modules/@stdlib/stats/base/dists/halfnormal/cdf/lib/index.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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/**
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* Half-normal distribution cumulative distribution function (CDF).
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*
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* @module @stdlib/stats/base/dists/halfnormal/cdf
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*
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* @example
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* var cdf = require( '@stdlib/stats/base/dists/halfnormal/cdf' );
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*
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* var y = cdf( 2.0, 1.0 );
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* // returns 0.9544997361036416
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*
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* var myCDF = cdf.factory( 2.0 );
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* y = myCDF( 1.0 );
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* // returns 0.3829249225480262
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*/
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// MODULES //
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var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
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var main = require( './main.js' );
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var factory = require( './factory.js' );
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// MAIN //
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setReadOnly( main, 'factory', factory );
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// EXPORTS //
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module.exports = main;

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