npm package: @stdlib/stats-base-dists-discrete-uniform-ctor
Description: Discrete uniform distribution constructor.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Discrete Uniform

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> Discrete uniform distribution constructor.

<!-- 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 -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### DiscreteUniform( \[a, b] )

Returns a [discrete uniform][discrete-uniform-distribution] distribution object.

```javascript
var discreteUniform = new DiscreteUniform();

var mu = discreteUniform.mean;
// returns 0.5
```

By default, `a = 0` and `b = 1`. To create a distribution having a different `a` (minimum support) and `b` (maximum support), provide the corresponding arguments.

```javascript
var discreteUniform = new DiscreteUniform( 2, 4 );

var mu = discreteUniform.mean;
// returns 3.0
```

* * *

## discreteUniform

A [discrete uniform][discrete-uniform-distribution] distribution object has the following properties and methods...

### Writable Properties

#### discreteUniform.a

Minimum support of the distribution. `a` **must** be an integer smaller than or equal to `b`.

```javascript
var discreteUniform = new DiscreteUniform( -2, 2 );

var a = discreteUniform.a;
// returns -2

discreteUniform.a = 0;

a = discreteUniform.a;
// returns 0
```

#### discreteUniform.b

Maximum support of the distribution. `b` **must** be an integer larger than or equal to `a`.

```javascript
var discreteUniform = new DiscreteUniform( 2, 4 );

var b = discreteUniform.b;
// returns 4

discreteUniform.b = 3;

b = discreteUniform.b;
// returns 3
```

* * *

### Computed Properties

#### DiscreteUniform.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var discreteUniform = new DiscreteUniform( 4, 12 );

var entropy = discreteUniform.entropy;
// returns ~2.197
```

#### DiscreteUniform.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var discreteUniform = new DiscreteUniform( 4, 12 );

var kurtosis = discreteUniform.kurtosis;
// returns -1.23
```

#### DiscreteUniform.prototype.mean

Returns the [expected value][expected-value].

```javascript
var discreteUniform = new DiscreteUniform( 4, 12 );

var mu = discreteUniform.mean;
// returns 8.0
```

#### DiscreteUniform.prototype.median

Returns the [median][median].

```javascript
var discreteUniform = new DiscreteUniform( 4, 12 );

var median = discreteUniform.median;
// returns 8.0
```

#### DiscreteUniform.prototype.skewness

Returns the [skewness][skewness].

```javascript
var discreteUniform = new DiscreteUniform( 4, 12 );

var skewness = discreteUniform.skewness;
// returns 0.0
```

#### DiscreteUniform.prototype.stdev

Returns the [standard deviation][standard-deviation].

```javascript
var discreteUniform = new DiscreteUniform( 4, 12 );

var s = discreteUniform.stdev;
// returns ~2.582
```

#### DiscreteUniform.prototype.variance

Returns the [variance][variance].

```javascript
var discreteUniform = new DiscreteUniform( 4, 12 );

var s2 = discreteUniform.variance;
// returns ~6.667
```

* * *

### Methods

#### DiscreteUniform.prototype.cdf( x )

Evaluates the [cumulative distribution function][cdf] (CDF).

```javascript
var discreteUniform = new DiscreteUniform( 2, 4 );

var y = discreteUniform.cdf( 2.5 );
// returns ~0.333
```

#### DiscreteUniform.prototype.logcdf( x )

Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).

```javascript
var discreteUniform = new DiscreteUniform( 2, 4 );

var y = discreteUniform.logcdf( 2.5 );
// returns ~-1.099
```

#### DiscreteUniform.prototype.logpmf( x )

Evaluates the natural logarithm of the [probability mass function][pmf] (PMF).

```javascript
var discreteUniform = new DiscreteUniform( 2, 4 );

var y = discreteUniform.logpmf( 4.0 );
// returns ~-1.099
```

#### DiscreteUniform.prototype.pmf( x )

Evaluates the [probability mass function][pmf] (PMF).

```javascript
var discreteUniform = new DiscreteUniform( 2, 4 );

var y = discreteUniform.pmf( 3, 0 );
// returns ~0.333
```

#### DiscreteUniform.prototype.quantile( p )

Evaluates the [quantile function][quantile-function] at probability `p`.

```javascript
var discreteUniform = new DiscreteUniform( 2, 4 );

var y = discreteUniform.quantile( 0.5 );
// returns 3.0

y = discreteUniform.quantile( 1.9 );
// returns NaN
```

</section>

<!-- /.usage -->

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<section class="notes">

</section>

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<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

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

var discreteUniform = new DiscreteUniform( -2, 2 );

var mu = discreteUniform.mean;
// returns 0.0

var median = discreteUniform.median;
// returns 0.0

var s2 = discreteUniform.variance;
// returns 2.0

var y = discreteUniform.cdf( 2.5 );
// returns 1.0
```

</section>

<!-- /.examples -->

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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].

#### Community

[![Chat][chat-image]][chat-url]

---

## 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-discrete-uniform-ctor/main/LICENSE

[discrete-uniform-distribution]: https://en.wikipedia.org/wiki/Discrete_uniform_distribution

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function

[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function

[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[expected-value]: https://en.wikipedia.org/wiki/Expected_value

[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis

[median]: https://en.wikipedia.org/wiki/Median

[skewness]: https://en.wikipedia.org/wiki/Skewness

[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation

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

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