# @stdlib/stats-base-dists-bernoulli-ctor

0.2.1 • Public • Published

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# Bernoulli

Bernoulli distribution constructor.

## Installation

`npm install @stdlib/stats-base-dists-bernoulli-ctor`

## Usage

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

#### Bernoulli( [p] )

Returns a Bernoulli distribution object.

```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.

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

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

## bernoulli

A Bernoulli distribution object has the following properties and methods...

### Writable Properties

#### bernoulli.p

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

```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.

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

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

#### Bernoulli.prototype.kurtosis

Returns the excess kurtosis.

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

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

#### Bernoulli.prototype.mean

Returns the median.

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

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

#### Bernoulli.prototype.median

Returns the median.

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

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

#### Bernoulli.prototype.mode

Returns the mode.

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

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

#### Bernoulli.prototype.skewness

Returns the skewness.

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

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

#### Bernoulli.prototype.stdev

Returns the standard deviation.

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

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

#### Bernoulli.prototype.variance

Returns the variance.

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

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

### Methods

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

Evaluates the cumulative distribution function (CDF).

```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).

```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).

```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 at probability `p`.

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

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

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

## Examples

```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```

## Notice

This package is part of 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, see the main project repository.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-bernoulli-ctor`

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