Probability Mass Function

Poisson distribution probability mass function (PMF).

The probability mass function (PMF) for a Poisson random variable is

where lambda > 0 is the mean parameter.

Installation

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

Usage

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

pmf( x, lambda )

Evaluates the probability mass function (PMF) of a Poisson distribution with mean parameter lambda.

var y = pmf( 4.0, 3.0 );
// returns ~0.168

y = pmf( 1.0, 3.0 );
// returns ~0.149

y = pmf( -1.0, 2.0 );
// returns 0.0

If provided NaN as any argument, the function returns NaN.

var y = pmf( NaN, 2.0 );
// returns NaN

y = pmf( 0.0, NaN );
// returns NaN

If provided a negative mean parameter lambda, the function returns NaN.

var y = pmf( 2.0, -1.0 );
// returns NaN

y = pmf( 4.0, -2.0 );
// returns NaN

If provided lambda = 0, the function evaluates the PMF of a degenerate distribution centered at 0.0.

var y = pmf( 2.0, 0.0 );
// returns 0.0

y = pmf( 0.0, 0.0 );
// returns 1.0

pmf.factory( lambda )

Returns a function for evaluating the probability mass function (PMF) of a Poisson distribution with mean parameter lambda.

var mypmf = pmf.factory( 1.0 );
var y = mypmf( 3.0 );
// returns ~0.061

y = mypmf( 1.0 );
// returns ~0.368

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var pmf = require( '@stdlib/stats-base-dists-poisson-pmf' );

var lambda;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = round( randu() * 10.0 );
    lambda = randu() * 10.0;
    y = pmf( x, lambda );
    console.log( 'x: %d, λ: %d, P(X=x;λ): %d', x, lambda.toFixed( 4 ), y.toFixed( 4 ) );
}

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

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.