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Poisson

Poisson distribution.

Installation

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

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

poisson

Poisson distribution.

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

The namespace contains the following distribution functions:

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

The namespace contains the following functions for calculating distribution properties:

• entropy( lambda ): Poisson distribution entropy.
• kurtosis( lambda ): Poisson distribution excess kurtosis.
• mean( lambda ): Poisson distribution expected value.
• median( lambda ): Poisson distribution median.
• mode( lambda ): Poisson distribution mode.
• skewness( lambda ): Poisson distribution skewness.
• stdev( lambda ): Poisson distribution standard deviation.
• variance( lambda ): Poisson distribution variance.

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

• Poisson( [lambda] ): Poisson distribution constructor.

var Poisson = require( '@stdlib/stats-base-dists-poisson' ).Poisson;

var dist = new Poisson( 2.0 );

var y = dist.pmf( 3.0 );
// returns ~0.18

y = dist.pmf( 2.3 );
// returns 0.0

Examples

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

/*
* Let's take a customer service center example: average rate of customer inquiries is 3 per hour.
* This situation can be modeled using a Poisson distribution with λ = 3
*/

var lambda = 3;

// Mean can be used to calculate the average number of inquiries per hour:
console.log( poisson.mean( lambda ) );
// => 3

// Standard deviation can be used to calculate the measure of the spread of inquiries around the mean:
console.log( poisson.stdev( lambda ) );
// => ~1.7321

// Variance can be used to calculate the variability of the number of inquiries:
console.log( poisson.variance( lambda ) );
// => 3

// PMF can be used to calculate specific number of inquiries in an hour:
console.log( poisson.pmf( 4, lambda ) );
// => ~0.1680

// CDF can be used to calculate probability up to certain number of inquiries in an hour:
console.log( poisson.cdf( 2, lambda ) );
// => ~0.4232

// Quantile can be used to calculate the number of inquiries at which you can be 80% confident that the actual number will not exceed.
console.log( poisson.quantile( 0.8, lambda ) );
// => 4

// MGF can be used for more advanced statistical analyses and generating moments of the distribution.
console.log( poisson.mgf( 1.0, lambda ) );
// => ~173.2690

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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.