Logarithm of Probability Mass Function

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

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

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where lambda > 0 is the mean parameter.

Usage

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

logpmf( x, lambda )

Evaluates the natural logarithm of the probability mass function (PMF) for a Poisson distribution with mean parameter lambda.

var y = logpmf( 4.0, 3.0 );
// returns ~-1.784

y = logpmf( 1.0, 3.0 );
// returns ~-1.901

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

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

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

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

If provided a negative mean parameter lambda, the function returns NaN.

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

y = logpmf( 4.0, -2.0 );
// returns NaN

If provided lambda = 0, the function evaluates the natural logarithm of the PMF of a degenerate distribution centered at 0.0.

var y = logpmf( 2.0, 0.0 );
// returns -Infinity

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

logpmf.factory( lambda )

Returns a function for evaluating the natural logarithm of the probability mass function (PMF) for a Poisson distribution with mean parameter lambda.

var mylogpmf = logpmf.factory( 1.0 );
var y = mylogpmf( 3.0 );
// returns ~-2.797

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

Examples

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

var lambda;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = round( randu() * 10.0 );
    lambda = randu() * 10.0;
    y = logpmf( x, lambda );
    console.log( 'x: %d, λ: %d, ln(P(X=x;λ)): %d', x, lambda.toFixed( 4 ), y.toFixed( 4 ) );
}