feat: initial implementation of stats/base/dists/halfnormal/cdf

lib/node_modules/@stdlib/stats/base/dists/halfnormal/cdf/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# Cumulative Distribution Function
+
+> [Half-normal][half-normal-distribution] distribution [cumulative distribution function][cdf].
+
+<section class="intro">
+
+The [cumulative distribution function][cdf] for a [half-normal][half-normal-distribution] random variable is
+
+```math
+F(x;\mu,\sigma) = \mathop{\mathrm{erf}}\left( \frac{x-\mu}{\sigma\sqrt{2}} \right)
+```
+
+where `µ` is the location parameter and `σ` is the scale parameter.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var cdf = require( '@stdlib/stats/base/dists/halfnormal/cdf' );
+```
+
+#### cdf( x, mu, sigma )
+
+Evaluates the [cumulative distribution function][cdf] (CDF) for a [half-normal][half-normal-distribution] distribution with parameters `mu` (location) and `sigma` (scale).
+
+```javascript
+var y = cdf( 2.0, 0.0, 1.0 );
+// returns 0.9544997361036416
+
+y = cdf( -1.0, 0.0, 1.0 );
+// returns 0.0
+
+y = cdf( -1.0, 2.0, 2.0 );
+// returns 0.0
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = cdf( NaN, 0.0, 1.0 );
+// returns NaN
+
+y = cdf( 0.0, NaN, 1.0 );
+// returns NaN
+
+y = cdf( 0.0, 0.0, NaN );
+// returns NaN
+```
+
+If provided `sigma < 0`, the function returns `NaN`.
+
+```javascript
+var y = cdf( 2.0, 0.0, -1.0 );
+// returns NaN
+```
+
+If provided `sigma = 0`, the function evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.
+
+```javascript
+var y = cdf( 2.0, 8.0, 0.0 );
+// returns 0.0
+
+y = cdf( 8.0, 8.0, 0.0 );
+// returns 1.0
+
+y = cdf( 10.0, 8.0, 0.0 );
+// returns 1.0
+```
+
+#### cdf.factory( mu, sigma )
+
+Returns a function for evaluating the [cumulative distribution function][cdf] of a [half-normal][half-normal-distribution] distribution with parameters `mu` and `sigma`.
+
+```javascript
+var mycdf = cdf.factory( 0.0, 1.0 );
+
+var y = mycdf( 2.0 );
+// returns 0.9544997361036416
+
+y = mycdf( -1.0 );
+// returns 0.0
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var cdf = require( '@stdlib/stats/base/dists/halfnormal/cdf' );
+
+var sigma;
+var mu;
+var x;
+var y;
+var i;
+
+for ( i = 0; i < 10; i++ ) {
+    x = randu() * 10.0;
+    mu = (randu() * 10.0) - 5.0;
+    sigma = randu() * 20.0;
+    y = cdf( x, mu, sigma );
+    console.log( 'x: %d, µ: %d, σ: %d, F(x;µ,σ): %d', x, mu, sigma, y );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
+
+[half-normal-distribution]: https://en.wikipedia.org/wiki/Half-normal_distribution
+
+[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pkg = require( './../package.json' ).name;
+var cdf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var sigma;
+	var len;
+	var mu;
+	var x;
+	var y;
+	var i;
+
+	len = 100;
+	x = uniform( len, 0.0, 100.0 );
+	mu = uniform( len, 0.0, 50.0 );
+	sigma = uniform( len, EPS, 20.0 + EPS );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = cdf( x[ i % len ], mu[ i % len ], sigma[ i % len ]);
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+':factory', function benchmark( b ) {
+	var mycdf;
+	var sigma;
+	var mu;
+	var x;
+	var y;
+	var i;
+
+	mu = 0.0;
+	sigma = 1.5;
+	mycdf = cdf.factory( mu, sigma );
+	x = uniform( 100, 0.0, 10.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = mycdf( x[ i % x.length ] );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

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

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