Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability mass function (PMF) for a binomial distribution.

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

logpmf( x, n, p )

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

var y = logpmf( 3.0, 20, 0.2 );
// returns ~-1.583

y = logpmf( 21.0, 20, 0.2 );
// returns -Infinity

y = logpmf( 5.0, 10, 0.4 );
// returns ~-1.606

y = logpmf( 0.0, 10, 0.4 );
// returns ~-5.108

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

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

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

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

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

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

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

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

logpmf.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 mylogpmf = logpmf.factory( 10, 0.5 );

var y = mylogpmf( 3.0 );
// returns ~-2.146

y = mylogpmf( 5.0 );
// returns ~-1.402

Examples

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

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 = logpmf( x, n, p );
    console.log( 'x: %d, n: %d, p: %d, ln(P(X = x;n,p)): %d', x, n, p.toFixed( 4 ), y.toFixed( 4 ) );
}