Probability Mass Function

Geometric distribution probability mass function (PMF).

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

probability left-parenthesis upper X equals x right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column left-parenthesis 1 minus p right-parenthesis Superscript x Baseline p 2nd Column for x equals 0 comma 1 comma 2 comma ellipsis 2nd Row 1st Column 0 2nd Column otherwise EndLayout

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.

Usage

var pmf = require( '@stdlib/math/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/math/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 ) );
}