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feat: add implementation of stats/base/dists/gilbrat/variance
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‎lib/node_modules/@stdlib/stats/base/dists/gilbrat/variance/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 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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# Variance
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> [gilbrat][gilbrat-distribution] distribution [variance][variance].
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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The [variance][variance] for a [gilbrat][gilbrat-distribution] random variable with scale parameter `σ > 0` is
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<!-- <equation class="equation" label="eq:gilbrat_variance" align="center" raw="\operatorname{Var}\left[ X \right] = e(e-1)" alt="Variance for a gilbrat distribution."> -->
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```math
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\operatorname{Var}\left[ X \right] = e(e-1)
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```
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<!-- <div class="equation" align="center" data-raw-text="\operatorname{Var}\left[ X \right] = e(e-1)" data-equation="eq:gilbrat_variance">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/gilbrat/variance/docs/img/gilbrat_variance.svg" alt="Variance for a gilbrat distribution.">
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<br>
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</div> -->
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="usage">
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## Usage
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```javascript
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var variance = require( '@stdlib/stats/base/dists/gilbrat/variance' );
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```
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#### variance( sigma )
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Returns the [variance][variance] for a [gilbrat][gilbrat-distribution] distribution with scale parameter `sigma`.
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```javascript
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var y = variance( 1.0 );
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// returns ~4.671
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y = variance( 4.0 );
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// returns ~4.671
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y = variance( 0.5 );
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// returns ~4.671
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```
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If provided `NaN`, the function returns `NaN`.
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```javascript
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var y = variance( 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 = variance( 0.0 );
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// returns NaN
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y = variance( -1.0 );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- Package usage examples. -->
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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 uniform = require( '@stdlib/random/array/uniform' );
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var logEachMap = require( '@stdlib/console/log-each-map' );
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var variance = require( '@stdlib/stats/base/dists/gilbrat/variance' );
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var opts = {
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'dtype': 'float64'
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};
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var sigma = uniform( 10, 0.1, 20.0, opts );
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logEachMap( 'σ: %lf, Var(X;σ): %lf', sigma, variance );
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```
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</section>
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<!-- /.examples -->
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<!-- 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. -->
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<section class="references">
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</section>
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<!-- /.references -->
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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 C API documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C API usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/stats/base/dists/gilbrat/variance.h"
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```
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#### stdlib_base_dists_gilbrat_variance( sigma )
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Returns the variance for a [gilbrat][gilbrat-distribution] distribution with scale parameter `sigma`.
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- **sigma**: `[in] double` scale parameter.
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```c
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double stdlib_base_dists_gilbrat_variance( const double sigma );
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/stats/base/dists/gilbrat/variance.h"
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#include <stdlib.h>
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#include <stdio.h>
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static double random_uniform( const double min, const double max ) {
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double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
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return min + ( v*(max-min) );
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}
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int main( void ) {
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double sigma;
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double y;
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int i;
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for ( i = 0; i < 10; i++ ) {
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sigma = random_uniform( 0.1, 20.0 );
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y = stdlib_base_dists_gilbrat_variance( sigma );
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printf( "σ: %lf, Var(X;σ): %lf\n", sigma, y );
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}
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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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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[gilbrat-distribution]: https://en.wikipedia.org/wiki/Gibrat's_law
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[variance]: https://en.wikipedia.org/wiki/variance
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/dists/gilbrat/variance/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) 2026 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 variance = 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 y;
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var i;
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sigma = uniform( 100, EPS, 20.0, {
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'dtype': 'float64'
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});
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = variance( sigma[ i%sigma.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/gilbrat/variance/benchmark/benchmark.native.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2026 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 resolve = require( 'path' ).resolve;
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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 tryRequire = require( '@stdlib/utils/try-require' );
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var EPS = require( '@stdlib/constants/float64/eps' );
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var format = require( '@stdlib/string/format' );
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var pkg = require( './../package.json' ).name;
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// VARIABLES //
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var variance = tryRequire( resolve( __dirname, './../lib/native.js' ) );
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var opts = {
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'skip': ( variance instanceof Error )
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};
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// MAIN //
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bench( format( '%s::native', pkg ), opts, function benchmark( b ) {
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var sigma;
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var y;
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var i;
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sigma = uniform( 100, EPS, 20.0, {
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'dtype': 'float64'
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});
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = variance( sigma[ i%sigma.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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});

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