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feat: initial implementation of @stdlib/stats/base/dists/halfnormal/cdf
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‎lib/node_modules/@stdlib/stats/base/dists/halfnormal/cdf/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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# Cumulative Distribution Function
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> [Half-normal][half-normal-distribution] distribution [cumulative distribution function][cdf].
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<section class="intro">
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The [cumulative distribution function][cdf] for a [half-normal][half-normal-distribution] random variable is
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```math
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F(x;\mu,\sigma) = \mathop{\mathrm{erf}}\left( \frac{x-\mu}{\sigma\sqrt{2}} \right)
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```
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where `µ` is the location parameter and `σ` is the scale parameter.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var cdf = require( '@stdlib/stats/base/dists/halfnormal/cdf' );
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```
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#### cdf( x, mu, sigma )
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Evaluates the [cumulative distribution function][cdf] (CDF) for a [half-normal][half-normal-distribution] distribution with parameters `mu` (location) and `sigma` (scale).
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```javascript
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var y = cdf( 2.0, 0.0, 1.0 );
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// returns 0.9544997361036416
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y = cdf( -1.0, 0.0, 1.0 );
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// returns 0.0
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y = cdf( -1.0, 2.0, 2.0 );
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// returns 0.0
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```
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If provided `NaN` as any argument, the function returns `NaN`.
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```javascript
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var y = cdf( NaN, 0.0, 1.0 );
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// returns NaN
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y = cdf( 0.0, NaN, 1.0 );
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// returns NaN
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y = cdf( 0.0, 0.0, NaN );
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// returns NaN
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```
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If provided `sigma < 0`, the function returns `NaN`.
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```javascript
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var y = cdf( 2.0, 0.0, -1.0 );
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// returns NaN
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```
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If provided `sigma = 0`, the function evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.
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```javascript
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var y = cdf( 2.0, 8.0, 0.0 );
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// returns 0.0
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y = cdf( 8.0, 8.0, 0.0 );
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// returns 1.0
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y = cdf( 10.0, 8.0, 0.0 );
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// returns 1.0
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```
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#### cdf.factory( mu, sigma )
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Returns a function for evaluating the [cumulative distribution function][cdf] of a [half-normal][half-normal-distribution] distribution with parameters `mu` and `sigma`.
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```javascript
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var mycdf = cdf.factory( 0.0, 1.0 );
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var y = mycdf( 2.0 );
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// returns 0.9544997361036416
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y = mycdf( -1.0 );
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// returns 0.0
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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 randu = require( '@stdlib/random/base/randu' );
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var cdf = require( '@stdlib/stats/base/dists/halfnormal/cdf' );
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var sigma;
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var mu;
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var x;
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var y;
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var i;
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for ( i = 0; i < 10; i++ ) {
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x = randu() * 10.0;
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mu = (randu() * 10.0) - 5.0;
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sigma = randu() * 20.0;
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y = cdf( x, mu, sigma );
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console.log( 'x: %d, µ: %d, σ: %d, F(x;µ,σ): %d', x, mu, sigma, y );
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}
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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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[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
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[half-normal-distribution]: https://en.wikipedia.org/wiki/Half-normal_distribution
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[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/dists/halfnormal/cdf/benchmark/benchmark.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 bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var EPS = require( '@stdlib/constants/float64/eps' );
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var pkg = require( './../package.json' ).name;
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var cdf = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var sigma;
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var len;
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var mu;
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var x;
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var y;
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var i;
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len = 100;
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x = uniform( len, 0.0, 100.0 );
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mu = uniform( len, 0.0, 50.0 );
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sigma = uniform( len, EPS, 20.0 + EPS );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = cdf( x[ i % len ], mu[ i % len ], sigma[ i % len ]);
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+':factory', function benchmark( b ) {
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var mycdf;
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var sigma;
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var mu;
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var x;
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var y;
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var i;
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mu = 0.0;
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sigma = 1.5;
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mycdf = cdf.factory( mu, sigma );
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x = uniform( 100, 0.0, 10.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = mycdf( x[ i % x.length ] );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/stats/base/dists/halfnormal/cdf/docs/repl.txt‎

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{{alias}}( x, μ, σ )
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Evaluates the cumulative distribution function (CDF) for a half-normal
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distribution with location `μ` and scale `σ` at a value `x`.
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If provided `NaN` as any argument, the function returns `NaN`.
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If provided `σ < 0`, the function returns `NaN`.
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Parameters
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----------
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x: number
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Input value.
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μ: number
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Location parameter.
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σ: number
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Scale parameter.
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Returns
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-------
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out: number
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Evaluated CDF.
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Examples
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--------
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> var y = {{alias}}( 2.0, 0.0, 1.0 )
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0.9544997361036416
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> y = {{alias}}( -1.0, 0.0, 1.0 )
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0.0
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> y = {{alias}}( -1.0, 2.0, 2.0 )
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0.0
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> y = {{alias}}( NaN, 0.0, 1.0 )
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NaN
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> y = {{alias}}( 0.0, NaN, 1.0 )
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NaN
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> y = {{alias}}( 0.0, 0.0, NaN )
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NaN
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// Negative scale parameter:
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> y = {{alias}}( 2.0, 0.0, -1.0 )
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NaN
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// Degenerate distribution centered at `μ` when `σ = 0.0`:
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> y = {{alias}}( 2.0, 8.0, 0.0 )
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0.0
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> y = {{alias}}( 8.0, 8.0, 0.0 )
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1.0
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> y = {{alias}}( 10.0, 8.0, 0.0 )
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1.0
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{{alias}}.factory( μ, σ )
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Returns a function for evaluating the cumulative distribution function (CDF)
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of a half-normal distribution with location `μ` and scale `σ`.
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Parameters
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----------
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μ: number
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Location parameter.
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σ: number
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Scale parameter.
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Returns
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-------
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cdf: Function
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Cumulative distribution function (CDF).
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Examples
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--------
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> var myCDF = {{alias}}.factory( 0.0, 1.0 );
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> var y = myCDF( 2.0 )
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0.9544997361036416
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See Also
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--------
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