Entropy
Cauchy distribution differential entropy.
The differential entropy for a Cauchy random variable with location parameter x0
and scale parameter Ɣ > 0
is
Usage
var entropy = require( '@stdlib/stats/base/dists/cauchy/entropy' );
entropy( x0, gamma )
Returns the differential entropy of a Cauchy distribution with location parameter x0
and scale parameter gamma
(in nats).
var v = entropy( 10.0, 5.0 );
// returns ~4.14
v = entropy( 7.0, 2.0 );
// returns ~3.224
If provided NaN
as any argument, the function returns NaN
.
var v = entropy( NaN, 5.0 );
// returns NaN
v = entropy( 20.0, NaN );
// returns NaN
If provided gamma <= 0
, the function returns NaN
.
var v = entropy( 1.0, -1.0 );
// returns NaN
v = entropy( 1.0, 0.0 );
// returns NaN
Examples
var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var entropy = require( '@stdlib/stats/base/dists/cauchy/entropy' );
var gamma;
var x0;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
x0 = randu() * 100.0;
gamma = ( randu()*10.0 ) + EPS;
v = entropy( x0, gamma );
console.log( 'x0: %d, γ: %d, h(X;x0,γ): %d', x0.toFixed( 4 ), gamma.toFixed( 4 ), v.toFixed( 4 ) );
}