npm package: @stdlib/stats-base-dists-rayleigh-variance
Description: Rayleigh distribution variance.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Variance

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> [Rayleigh][rayleigh-distribution] distribution [variance][variance].

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<section class="intro">

The [variance][variance] for a [Rayleigh][rayleigh-distribution] random variable is

<!-- <equation class="equation" label="eq:rayleigh_variance" align="center" raw="\operatorname{Var}\left( X \right) = \frac{4-\pi }{2}\sigma^{2}" alt="Variance for a Rayleigh distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Var}\left( X \right) = \frac{4-\pi }{2}\sigma^{2}" data-equation="eq:rayleigh_variance">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/rayleigh/variance/docs/img/equation_rayleigh_variance.svg" alt="Variance for a Rayleigh distribution.">
    <br>
</div>

<!-- </equation> -->

where `σ > 0` is the scale parameter.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-rayleigh-variance
```

</section>

<section class="usage">

## Usage

```javascript
var variance = require( '@stdlib/stats-base-dists-rayleigh-variance' );
```

#### variance( sigma )

Returns the [variance][variance] of a [Rayleigh][rayleigh-distribution] distribution with scale `sigma`.

```javascript
var y = variance( 9.0 );
// returns ~34.765

y = variance( 3.5 );
// returns ~5.258
```

If provided `sigma < 0`, the function returns `NaN`.

```javascript
var 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-rayleigh-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 -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/base/dists/rayleigh/variance.h"
```

#### stdlib_base_dists_rayleigh_variance( sigma )

Returns the variance of a Rayleigh distribution.

```c
double out = stdlib_base_dists_rayleigh_variance( 9.0 );
// returns ~34.765
```

The function accepts the following arguments:

-   **sigma**: `[in] double` scale parameter.

```c
double stdlib_base_dists_rayleigh_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/rayleigh/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 < 25; i++ ) {
        sigma = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_rayleigh_variance( sigma );
        printf( "σ: %lf, Var(X;σ): %lf\n", sigma, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="references">

</section>

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<section class="related">

</section>

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-rayleigh-variance/main/LICENSE

[rayleigh-distribution]: https://en.wikipedia.org/wiki/Rayleigh_distribution

[variance]: https://en.wikipedia.org/wiki/Variance

</section>

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