Entropy

Poisson distribution entropy.

The entropy (in nats) for a Poisson random variable is

upper H left-parenthesis upper X right-parenthesis equals lamda left-bracket 1 minus log left-parenthesis lamda right-parenthesis right-bracket plus e Superscript negative lamda Baseline sigma-summation Underscript k equals 0 Overscript normal infinity Endscripts StartFraction lamda Superscript k Baseline log left-parenthesis k factorial right-parenthesis Over k factorial EndFraction

where λ is the mean parameter.

Usage

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

entropy( lambda )

Returns the entropy of a Poisson distribution with mean parameter lambda (in nats).

var v = entropy( 9.0 );
// returns ~2.508

v = entropy( 0.5 );
// returns ~0.928

If provided lambda < 0, the function returns NaN.

var v = entropy( -1.0 );
// returns NaN

Examples

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

var lambda;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    lambda = randu() * 20.0;
    v = entropy( lambda );
    console.log( 'λ: %d, H(X;λ): %d', lambda.toFixed( 4 ), v.toFixed( 4 ) );
}