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Bernoulli

Bernoulli distribution constructor.

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.