Entropy

Weibull distribution differential entropy.

The differential entropy (in nats) for a Weibull random variable is

h left-parenthesis upper X right-parenthesis equals gamma left-parenthesis 1 minus 1 slash k right-parenthesis plus ln left-parenthesis lamda slash k right-parenthesis plus 1

where λ > 0 is the shape parameter, k > 0 is the scale parameter, and Ɣ denotes the Euler–Mascheroni constant.

Usage

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

entropy( k, lambda )

Returns the differential entropy of a Weibull distribution with shape parameter k and scale parameter lambda (in nats).

var v = entropy( 1.0, 1.0 );
// returns 1.0

v = entropy( 4.0, 12.0 );
// returns ~2.532

v = entropy( 8.0, 2.0 );
// returns ~0.119

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

var v = entropy( NaN, 2.0 );
// returns NaN

v = entropy( 2.0, NaN );
// returns NaN

If provided k <= 0, the function returns NaN.

var v = entropy( 0.0, 1.0 );
// returns NaN

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

If provided lambda <= 0, the function returns NaN.

var v = entropy( 1.0, 0.0 );
// returns NaN

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

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var entropy = require( '@stdlib/math/base/dists/weibull/entropy' );

var lambda;
var k;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    k = ( randu()*10.0 ) + EPS;
    lambda = ( randu()*10.0 ) + EPS;
    v = entropy( k, lambda );
    console.log( 'k: %d, λ: %d, h(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
}