feat: implementation of variance for halfnormal distribution

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

@@ -0,0 +1,245 @@
+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+
+-->
+
+# Variance
+
+> [Half-normal][half-normal-distribution] distribution [variance][variance].
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+The [variance][variance] for a [half-normal][half-normal-distribution] random variable with scale parameter `σ > 0` is
+
+<!-- <equation class="equation" label="eq:halfnormal_variance" align="center" raw="\operatorname{Var}\left[ X \right] = \sigma^{2} \left(1 - \frac{2}{\pi}\right)" alt="Variance for a half-normal distribution."> -->
+
+```math
+\operatorname{Var}\left[ X \right] = \sigma^{2} \left(1 - \frac{2}{\pi}\right)
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\operatorname{Var}\left[ X \right] = \sigma^{2} \left(1 - \frac{2}{\pi}\right)" data-equation="eq:halfnormal_variance">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/img/equation_halfnormal_variance.svg" alt="Variance for a half-normal distribution.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var variance = require( '@stdlib/stats/base/dists/halfnormal/variance' );
+```
+
+#### variance( sigma )
+
+Returns the [variance][variance] for a [half-normal][half-normal-distribution] distribution with scale parameter `sigma`.
+
+```javascript
+var y = variance( 1.0 );
+// returns ~0.363
+
+y = variance( 4.0 );
+// returns ~5.814083642118698
+
+y = variance( 0.5 );
+// returns ~0.091
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = variance( NaN );
+// returns NaN
+```
+
+If provided `sigma <= 0`, the function returns `NaN`.
+
+```javascript
+var y = variance( 0.0 );
+// returns NaN
+
+y = variance( -1.0 );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- Package usage examples. -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var variance = require( '@stdlib/stats/base/dists/halfnormal/variance' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var sigma = uniform( 10, 0.0, 20.0, opts );
+
+logEachMap( 'σ: %0.4f, Var(X;σ): %0.4f', sigma, variance );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for C API documentation. -->
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C API usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/stats/base/dists/halfnormal/variance.h"
+```
+
+#### stdlib_base_dists_halfnormal_variance( sigma )
+
+Returns the variance for a [half-normal][half-normal-distribution] distribution with scale parameter `sigma`.
+
+-   **sigma**: `[in] double` scale parameter.
+-   **return**: `[out] double` variance.
+
+```c
+double stdlib_base_dists_halfnormal_variance( const double sigma );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/stats/base/dists/halfnormal/variance.h"
+#include <stdlib.h>
+#include <stdio.h>
+
+static double random_uniform( const double min, const double max ) {
+    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
+    return min + ( v*(max-min) );
+}
+
+int main( void ) {
+    double sigma;
+    double y;
+    int i;
+
+    for ( i = 0; i < 10; i++ ) {
+        sigma = random_uniform( 0.1, 20.0 );
+        y = stdlib_base_dists_halfnormal_variance( sigma );
+        printf( "σ: %.4f, Var(X;σ): %.4f\n", sigma, y );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- 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">
+
+[half-normal-distribution]: https://en.wikipedia.org/wiki/Half-normal_distribution
+
+[variance]: https://en.wikipedia.org/wiki/Variance
+
+</section>
+
+<!-- /.links -->

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

@@ -0,0 +1,52 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 randu = require( '@stdlib/random/base/randu' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pkg = require( './../package.json' ).name;
+var variance = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var sigma;
+	var y;
+	var i;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		sigma = ( randu()*20.0 ) + EPS;
+		y = variance( sigma );
+		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/variance/benchmark/benchmark.native.js

@@ -0,0 +1,67 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var Float64Array = require( '@stdlib/array/float64' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var variance = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( variance instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+	var sigma;
+	var len;
+	var y;
+	var i;
+
+	len = 100;
+	sigma = new Float64Array( len );
+	for ( i = 0; i < len; i++ ) {
+		sigma[ i ] = uniform( EPS, 20.0 );
+	}
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = variance( 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();
+});