Probability Density Function

Binomial distribution probability mass function (PMF).

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

f left-parenthesis x semicolon n comma p right-parenthesis equals upper P left-parenthesis upper X equals x semicolon n comma p right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartBinomialOrMatrix n Choose x EndBinomialOrMatrix p Superscript x Baseline left-parenthesis 1 minus p right-parenthesis Superscript n minus x Baseline 2nd Column for x equals 0 comma 1 comma 2 comma ellipsis 2nd Row 1st Column 0 2nd Column otherwise EndLayout

where n is the number of trials and 0 <= p <= 1 is the success probability.

Usage

var pmf = require( '@stdlib/math/base/dists/binomial/pmf' );

pmf( x, n, p )

Evaluates the probability mass function (PMF) for a binomial distribution with number of trials n and success probability p.

var y = pmf( 3.0, 20, 0.2 );
// returns ~0.205

y = pmf( 21.0, 20, 0.2 );
// returns 0.0

y = pmf( 5.0, 10, 0.4 );
// returns ~0.201

y = pmf( 0.0, 10, 0.4 );
// returns ~0.06

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

var y = pmf( NaN, 20, 0.5 );
// returns NaN

y = pmf( 0.0, NaN, 0.5 );
// returns NaN

y = pmf( 0.0, 20, NaN );
// returns NaN

If provided a number of trials n which is not a nonnegative integer, the function returns NaN.

var y = pmf( 2.0, 1.5, 0.5 );
// returns NaN

y = pmf( 2.0, -2.0, 0.5 );
// returns NaN

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

var y = pmf( 2.0, 20, -1.0 );
// returns NaN

y = pmf( 2.0, 20, 1.5 );
// returns NaN

pmf.factory( n, p )

Returns a function for evaluating the probability mass function (PMF) of a binomial distribution with number of trials n and success probability p.

var mypmf = pmf.factory( 10, 0.5 );

var y = mypmf( 3.0 );
// returns ~0.117

y = mypmf( 5.0 );
// returns ~0.246

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    x = round( randu() * 20.0 );
    n = round( randu() * 100.0 );
    p = randu();
    y = pmf( x, n, p );
    console.log( 'x: %d, n: %d, p: %d, P(X = x;n,p): %d', x, n, p.toFixed( 4 ), y.toFixed( 4 ) );
}