npm package: @stdlib/stats-base-dists-discrete-uniform-variance
Description: Discrete uniform distribution variance.
Author: The Stdlib Authors
Latest version: 0.2.1

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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] -->

> [Discrete uniform][discrete-uniform-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 [discrete uniform][discrete-uniform-distribution] random variable is

<!-- <equation class="equation" label="eq:discrete_uniform_variance" align="center" raw="\operatorname{Var}\left( X \right) = \frac{\left( b - a + 1 \right)^2 - 1}{12}" alt="Variance for a discrete uniform distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Var}\left( X \right) = \frac{\left( b - a + 1 \right)^2 - 1}{12}" data-equation="eq:discrete_uniform_variance">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/discrete-uniform/variance/docs/img/equation_discrete_uniform_variance.svg" alt="Variance for a discrete uniform distribution.">
    <br>
</div>

<!-- </equation> -->

where `a` is the minimum support and `b` the maximum support of the distribution.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### variance( a, b )

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

```javascript
var v = variance( 0, 1 );
// returns ~0.25

v = variance( 4, 12 );
// returns ~6.667

v = variance( -4, 4 );
// returns ~6.667
```

If `a` or `b` is not an integer value, the function returns `NaN`.

```javascript
var v = variance( 0.1, 2 );
// returns NaN

v = variance( 0, 2.2 );
// returns NaN

v = variance( NaN, 2 );
// returns NaN

v = variance( 2, NaN );
// returns NaN
```

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

```javascript
var v = variance( 3, 2 );
// returns NaN

v = variance( -1, -2 );
// 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 randint = require( '@stdlib/random-base-discrete-uniform' );
var variance = require( '@stdlib/stats-base-dists-discrete-uniform-variance' );

var randa = randint.factory( 0, 10 );
var randb = randint.factory();
var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = randa();
    b = randb( a, a+randa() );
    v = variance( a, b );
    console.log( 'a: %d, b: %d, Var(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}
```

</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/discrete-uniform/variance.h"
```

#### stdlib_base_dists_discrete_uniform_variance( a, b )

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

```c
double out = stdlib_base_dists_discrete_uniform_variance( 0, 1 );
// returns ~0.25
```

The function accepts the following arguments:

-   **a**: `[in] int32_t` minimum support.
-   **b**: `[in] int32_t` maximum support.

```c
double stdlib_base_dists_discrete_uniform_variance( const int32_t a, const int32_t b );
```

</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/discrete-uniform/variance.h"
#include "stdlib/math/base/special/round.h"
#include <stdint.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 ) {
    int32_t a;
    int32_t b;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        a = stdlib_base_round( random_uniform( 0.0, 10.0 ) );
        b = stdlib_base_round( random_uniform( 0.0, 10.0 ) ) + a;
        y = stdlib_base_dists_discrete_uniform_variance( a, b );
        printf( "a: %d, b: %d, Var(X;a,b): %lf\n", a, b, 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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[discrete-uniform-distribution]: https://en.wikipedia.org/wiki/Discrete_uniform_distribution

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

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