Probability Mass Function

Poisson distribution probability mass function (PMF).

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

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where lambda > 0 is the mean parameter.

Usage

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

pmf( x, lambda )

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

var y = pmf( 4.0, 3.0 );
// returns ~0.168

y = pmf( 1.0, 3.0 );
// returns ~0.149

y = pmf( -1.0, 2.0 );
// returns 0.0

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

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

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

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

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

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

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

var y = pmf( 2.0, 0.0 );
// returns 0.0

y = pmf( 0.0, 0.0 );
// returns 1.0

pmf.factory( lambda )

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

var mypmf = pmf.factory( 1.0 );
var y = mypmf( 3.0 );
// returns ~0.061

y = mypmf( 1.0 );
// returns ~0.368

Examples

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

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

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