Cumulative Distribution Function

Poisson distribution cumulative distribution function.

The cumulative distribution function for a Poisson random variable is

where lambda is the mean parameter. Internally, the module evaluates the CDF by evaluating the upper regularized gamma function at input values lambda and floor( x ) + 1.

Installation

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

Usage

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

cdf( x, lambda )

Evaluates the cumulative distribution function for a Poisson distribution with mean parameter lambda.

var y = cdf( 2.0, 0.5 );
// returns ~0.986

y = cdf( 2.0, 10.0 );
// returns ~0.003

y = cdf( -1.0, 4.0 );
// returns 0.0

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

var y = cdf( NaN, 1.0 );
// returns NaN

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

If provided lambda < 0, the function returns NaN.

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

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

var y = cdf( -2.0, 0.0 );
// returns 0.0

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

y = cdf( 10.0, 0.0 );
// returns 1.0

cdf.factory( lambda )

Returns a function for evaluating the cumulative distribution function of a Poisson distribution with mean parameter lambda.

var mycdf = cdf.factory( 5.0 );
var y = mycdf( 3.0 );
// returns ~0.265

y = mycdf( 8.0 );
// returns ~0.932

Examples

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

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

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