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Probability Mass Function

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Geometric distribution probability mass function (PMF).

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

Probability mass function (PMF) for a geometric distribution.

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.


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


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


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 ) );


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.






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