Logarithm of Probability Mass Function

Geometric distribution logarithm of 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.

Usage

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

logpmf( x, p )

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

var y = logpmf( 4.0, 0.3 );
// returns ~-2.631

y = logpmf( 2.0, 0.7 );
// returns ~-2.765

y = logpmf( -1.0, 0.5 );
// returns -Infinity

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

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

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

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

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

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

logpmf.factory( p )

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

var mylogpmf = logpmf.factory( 0.5 );
var y = mylogpmf( 3.0 );
// returns ~-2.773

y = mylogpmf( 1.0 );
// returns ~-1.386

Notes

In virtually all cases, using the logpmf or logcdf functions is preferable to manually computing the logarithm of the pmf or cdf, respectively, since the latter is prone to overflow and underflow.

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    x = round( randu() * 5.0 );
    p = randu();
    y = logpmf( x, p );
    console.log( 'x: %d, p: %d, ln( P( X = x; p ) ): %d', x, p.toFixed( 4 ), y.toFixed( 4 ) );
}