Probability Mass Function

Geometric distribution probability mass function (PMF).

The probability mass function (PMF) for a geometric random variable is defined as

where 0 <= p <= 1 is the success probability. The random variable X denotes the number of failures until the first success in a sequence of independent Bernoulli trials.

Installation

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

Usage

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

pmf( x, p )

Evaluates the probability mass function (PMF) of a geometric distribution with success probability 0 <= p <= 1.

var y = pmf( 4.0, 0.3 );
// returns ~0.072

y = pmf( 2.0, 0.7 );
// returns ~0.063

y = pmf( -1.0, 0.5 );
// returns 0.0

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

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

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

If provided a success probability p outside of the interval [0,1], the function returns NaN.

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

y = pmf( 2.0, 1.5 );
// returns NaN

pmf.factory( p )

Returns a function for evaluating the probability mass function (PMF) of a geometric distribution with success probability 0 <= p <= 1.

var mypmf = pmf.factory( 0.5 );
var y = mypmf( 3.0 );
// returns 0.0625

y = mypmf( 1.0 );
// returns 0.25

Examples

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

var p;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = round( randu() * 5.0 );
    p = randu();
    y = pmf( x, p );
    console.log( 'x: %d, p: %d, P( X = x; p ): %d', x, p.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.