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Binomial

Binomial distribution.

Installation

npm install @stdlib/stats-base-dists-binomial

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 binomial = require( '@stdlib/stats-base-dists-binomial' );

binomial

Binomial distribution.

var dist = binomial;
// returns {...}

The namespace contains the following distribution functions:

• cdf( x, n, p ): binomial distribution cumulative distribution function.
• logpmf( x, n, p ): evaluate the natural logarithm of the probability mass function (PMF) for a binomial distribution.
• mgf( t, n, p ): binomial distribution moment-generating function (MGF).
• pmf( x, n, p ): binomial distribution probability mass function (PMF).
• quantile( r, n, p ): binomial distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

• entropy( n, p ): binomial distribution entropy.
• kurtosis( n, p ): binomial distribution excess kurtosis.
• mean( n, p ): binomial distribution expected value.
• median( n, p ): binomial distribution median.
• mode( n, p ): binomial distribution mode.
• skewness( n, p ): binomial distribution skewness.
• stdev( n, p ): binomial distribution standard deviation.
• variance( n, p ): binomial distribution variance.

The namespace contains a constructor function for creating a binomial distribution object.

• Binomial( [n, p] ): binomial distribution constructor.

var Binomial = require( '@stdlib/stats-base-dists-binomial' ).Binomial;
var dist = new Binomial( 10, 0.4 );

var mu = dist.mean;
// returns 4

Examples

var binomial = require( '@stdlib/stats-base-dists-binomial' );

/*
* Let's take an example of rolling a fair dice 10 times and counting the number of times a 6 is rolled.
* This situation can be modeled using a Binomial distribution with n = 10 and p = 1/6
*/

var n = 10;
var p = 1/6;

// Mean can be used to calculate the average number of times a 6 is rolled:
console.log( binomial.mean( n, p ) );
// => ~1.6667

// PMF can be used to calculate the probability of getting a certain number of 6s (say 3 sixes):
console.log( binomial.pmf( 3, n, p ) );
// => ~0.1550

// CDF can be used to calculate probability up to certain number of 6s (say up to 3 sixes):
console.log( binomial.cdf( 3, n, p ) );
// => ~0.9303

// Quantile can be used to calculate the number of 6s at which you can be 80% confident that the actual number will not exceed.
console.log( binomial.quantile( 0.8, n, p ) );
// => 3

// Standard deviation can be used to calculate the measure of the spread of 6s around the mean:
console.log( binomial.stdev( n, p ) );
// => ~1.1785

// Skewness can be used to calculate the asymmetry of the distribution of 6s:
console.log( binomial.skewness( n, p ) );
// => ~0.5657

// MGF can be used for more advanced statistical analyses and generating moments of the distribution:
console.log( binomial.mgf( 0.5, n, p ) );
// => ~2.7917

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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 © 2016-2024. The Stdlib Authors.