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

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# Bernoulli

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

> Bernoulli 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-bernoulli-ctor
```

</section>

<section class="usage">

## Usage

```javascript
var Bernoulli = require( '@stdlib/stats-base-dists-bernoulli-ctor' );
```

#### Bernoulli( \[p] )

Returns a [Bernoulli][bernoulli-distribution] distribution object.

```javascript
var bernoulli = new Bernoulli();

var mean = bernoulli.mean;
// returns 0.5
```

By default, `p = 0.5`. To create a distribution having a different success probability `p`, provide a parameter value.

```javascript
var bernoulli = new Bernoulli( 0.2 );

var mean = bernoulli.mean;
// returns 0.2
```

* * *

## bernoulli

A [Bernoulli][bernoulli-distribution] distribution object has the following properties and methods...

### Writable Properties

#### bernoulli.p

Success probability of the distribution. `p` **must** be a probability.

```javascript
var bernoulli = new Bernoulli( 0.2 );

var p = bernoulli.p;
// returns 0.2

bernoulli.p = 0.3;

p = bernoulli.p;
// returns 0.3
```

* * *

### Computed Properties

#### Bernoulli.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var bernoulli = new Bernoulli( 0.4 );

var entropy = bernoulli.entropy;
// returns ~0.673
```

#### Bernoulli.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var bernoulli = new Bernoulli( 0.4 );

var kurtosis = bernoulli.kurtosis;
// returns ~-1.833
```

#### Bernoulli.prototype.mean

Returns the [median][expected-value].

```javascript
var bernoulli = new Bernoulli( 0.4 );

var mu = bernoulli.mean;
// returns 0.4
```

#### Bernoulli.prototype.median

Returns the [median][median].

```javascript
var bernoulli = new Bernoulli( 0.4 );

var median = bernoulli.median;
// returns 0.0
```

#### Bernoulli.prototype.mode

Returns the [mode][mode].

```javascript
var bernoulli = new Bernoulli( 0.4 );

var mode = bernoulli.mode;
// returns 0.0
```

#### Bernoulli.prototype.skewness

Returns the [skewness][skewness].

```javascript
var bernoulli = new Bernoulli( 0.4 );

var skewness = bernoulli.skewness;
// returns ~0.408
```

#### Bernoulli.prototype.stdev

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

```javascript
var bernoulli = new Bernoulli( 0.4 );

var s = bernoulli.stdev;
// returns ~0.49
```

#### Bernoulli.prototype.variance

Returns the [variance][variance].

```javascript
var bernoulli = new Bernoulli( 0.4 );

var s2 = bernoulli.variance;
// returns 0.24
```

* * *

### Methods

#### Bernoulli.prototype.cdf( x )

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

```javascript
var bernoulli = new Bernoulli( 0.2 );

var y = bernoulli.cdf( 0.5 );
// returns 0.8
```

#### Bernoulli.prototype.mgf( t )

Evaluates the [moment-generating function][mgf] (MGF).

```javascript
var bernoulli = new Bernoulli( 0.2 );

var y = bernoulli.mgf( -3.0 );
// returns ~0.81
```

#### Bernoulli.prototype.pmf( x )

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

```javascript
var bernoulli = new Bernoulli( 0.2 );

var y = bernoulli.pmf( 0.0 );
// returns 0.8

y = bernoulli.pmf( 1.0 );
// returns 0.2
```

#### Bernoulli.prototype.quantile( p )

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

```javascript
var bernoulli = new Bernoulli( 0.2 );

var y = bernoulli.quantile( 0.5 );
// returns 0

y = bernoulli.quantile( 0.9 );
// returns 1
```

</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 Bernoulli = require( '@stdlib/stats-base-dists-bernoulli-ctor' );

var bernoulli = new Bernoulli( 0.5 );

var mu = bernoulli.mean;
// returns 0.5

var s2 = bernoulli.variance;
// returns 0.25

var y = bernoulli.cdf( 2.0 );
// returns 1.0
```

</section>

<!-- /.examples -->

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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

[![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-bernoulli-ctor/main/LICENSE

[bernoulli-distribution]: https://en.wikipedia.org/wiki/Bernoulli_distribution

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

[mgf]: https://en.wikipedia.org/wiki/Moment-generating_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

[mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29

[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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