Logarithm of Probability Mass Function

Evaluate the logarithm of the probability mass function (PMF) for a Planck (discrete exponential) distribution.

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

where λ is the shape parameter and x denotes the count of events in a quantized system.

Usage

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

logpmf( x, lambda )

Evaluates the logarithm of the probability mass function (PMF) of a Planck (discrete exponential) distribution with shape parameter lambda.

var y = logpmf( 4.0, 0.3 );
// returns ~-2.5502

y = logpmf( 2.0, 1.7 );
// returns ~-3.6017

y = logpmf( -1.0, 2.5 );
// 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 shape parameter lambda which is nonpositive number, the function returns NaN.

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

logpmf.factory( lambda )

Returns a function for evaluating the logarithm of the probability mass function (PMF) of a Planck (discrete exponential) distribution with shape parameter lambda.

var mylogpmf = logpmf.factory( 0.5 );
var y = mylogpmf( 3.0 );
// returns ~-2.4328

y = mylogpmf( 1.0 );
// returns ~-1.4328

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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var uniform = require( '@stdlib/random/array/uniform' );
var logpmf = require( '@stdlib/stats/base/dists/planck/logpmf' );

var x = discreteUniform( 10, 0, 5 );
var lambda = uniform( 10, 0.1, 5.0 );

var y;
var i;
for ( i = 0; i < lambda.length; i++ ) {
    y = logpmf( x[ i ], lambda[ i ] );
    console.log( 'x: %d, λ: %d, ln( P( X = x; λ ) ): %d', x[ i ], lambda[ i ].toFixed( 4 ), y.toFixed( 4 ) );
}