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Poisson

Poisson distribution constructor.

Installation

npm install @stdlib/stats-base-dists-poisson-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 Poisson = require( '@stdlib/stats-base-dists-poisson-ctor' );

Poisson( [lambda] )

Returns an Poisson distribution object.

var poisson = new Poisson();

var lambda = poisson.mean;
// returns 1.0

By default, lambda = 1.0. To create a distribution having a different mean parameter lambda, provide a parameter value.

var poisson = new Poisson( 4.0 );

var lambda = poisson.mean;
// returns 4.0

---

poisson

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

Writable Properties

poisson.lambda

Mean parameter of the distribution. lambda must be a positive number.

var poisson = new Poisson( 2.0 );

var lambda = poisson.lambda;
// returns 2.0

poisson.lambda = 3.0;

lambda = poisson.lambda;
// returns 3.0

---

Computed Properties

Poisson.prototype.entropy

Returns the differential entropy.

var poisson = new Poisson( 4.0 );

var entropy = poisson.entropy;
// returns ~2.087

Poisson.prototype.kurtosis

Returns the excess kurtosis.

var poisson = new Poisson( 4.0 );

var kurtosis = poisson.kurtosis;
// returns 0.25

Poisson.prototype.mean

Returns the median.

var poisson = new Poisson( 4.0 );

var mu = poisson.mean;
// returns 4.0

Poisson.prototype.median

Returns the median.

var poisson = new Poisson( 4.0 );

var median = poisson.median;
// returns 4.0

Poisson.prototype.mode

Returns the mode.

var poisson = new Poisson( 4.0 );

var mode = poisson.mode;
// returns 4.0

Poisson.prototype.skewness

Returns the skewness.

var poisson = new Poisson( 4.0 );

var skewness = poisson.skewness;
// returns 0.5

Poisson.prototype.stdev

Returns the standard deviation.

var poisson = new Poisson( 4.0 );

var s = poisson.stdev;
// returns 2.0

Poisson.prototype.variance

Returns the variance.

var poisson = new Poisson( 4.0 );

var s2 = poisson.variance;
// returns 4.0

---

Methods

Poisson.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var poisson = new Poisson( 2.0 );

var y = poisson.cdf( 0.5 );
// returns ~0.135

Poisson.prototype.logpmf( x )

Evaluates the natural logarithm of the probability mass function (PMF).

var poisson = new Poisson( 2.0 );

var y = poisson.logpmf( 3.0 );
// returns ~-1.712

y = poisson.logpmf( 2.3 );
// returns -Infinity

Poisson.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var poisson = new Poisson( 2.0 );

var y = poisson.mgf( 0.5 );
// returns ~3.66

Poisson.prototype.pmf( x )

Evaluates the probability mass function (PMF).

var poisson = new Poisson( 2.0 );

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

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

Poisson.prototype.quantile( p )

Evaluates the quantile function at probability p.

var poisson = new Poisson( 2.0 );

var y = poisson.quantile( 0.5 );
// returns 2.0

y = poisson.quantile( 1.9 );
// returns NaN

---

Examples

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

var poisson = new Poisson( 2.0 );

var mu = poisson.mean;
// returns 2.0

var mode = poisson.mode;
// returns 2.0

var s2 = poisson.variance;
// returns 2.0

var y = poisson.cdf( 0.8 );
// returns ~0.135

---

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.