npm package: @stdlib/stats-base-dists-arcsine-variance
Description: Arcsine distribution variance.
Author: The Stdlib Authors
Latest version: 0.2.3

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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] -->

> [Arcsine][arcsine-distribution] distribution [variance][variance].

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<section class="intro">

The [variance][variance] for an [arcsine][arcsine-distribution] random variable with minimum support `a` and maximum support `b` is

<!-- <equation class="equation" label="eq:arcsine_variance" align="center" raw="\operatorname{Var}\left( X \right) = {\tfrac {1}{8}}(b-a)^{2}" alt="Variance for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Var}\left( X \right) = {\tfrac {1}{8}}(b-a)^{2}" data-equation="eq:arcsine_variance">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/variance/docs/img/equation_arcsine_variance.svg" alt="Variance for an arcsine distribution.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### variance( a, b )

Returns the [variance][variance] of an [arcsine][arcsine-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).

```javascript
var v = variance( 0.0, 1.0 );
// returns ~0.125

v = variance( 4.0, 12.0 );
// returns 8.0

v = variance( 2.0, 8.0 );
// returns ~4.5
```

If provided `NaN` as any argument, the function returns `NaN`.

```javascript
var v = variance( NaN, 2.0 );
// returns NaN

v = variance( 2.0, NaN );
// returns NaN
```

If provided `a >= b`, the function returns `NaN`.

```javascript
var v = variance( 3.0, 2.0 );
// returns NaN

v = variance( 3.0, 3.0 );
// 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>

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<!-- 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-arcsine-variance' );

var opts = {
    'dtype': 'float64'
};
var a = uniform( 25, 0.0, 10.0, opts );
var b = uniform( a.length, 10.0, 20.0, opts );

logEachMap( 'a: %0.4f, b: %0.4f, Var(X;a,b): %0.4f', a, b, 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/arcsine/variance.h"
```

#### stdlib_base_dists_arcsine_variance( a, b )

Returns the variance of an arcsine distribution.

```c
double out = stdlib_base_dists_arcsine_variance( 0.0, 1.0 );
// returns ~0.125
```

The function accepts the following arguments:

-   **a**: `[in] double` minimum support.
-   **b**: `[in] double` maximum support.

```c
double stdlib_base_dists_arcsine_variance( const double a, const double b );
```

</section>

<!-- /.usage -->

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<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/arcsine/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 a;
    double b;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        a = random_uniform( 0.0, 10.0 );
        b = random_uniform( a, a+10.0 );
        y = stdlib_base_dists_arcsine_variance( a, b );
        printf( "a: %lf, b: %lf, Var(X;a,b): %lf\n", a, b, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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</section>

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</section>

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* * *

## 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].

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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-arcsine-variance/main/LICENSE

[arcsine-distribution]: https://en.wikipedia.org/wiki/Arcsine_distribution

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

</section>

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