# Entropy

Pareto (Type I) distribution differential entropy.

The differential entropy (in nats) for a Pareto (Type I) random variable is

where α > 0 is the shape parameter and β > 0 is the scale parameter.

## Usage

var entropy = require( '@stdlib/math/base/dists/pareto-type1/entropy' );


#### entropy( alpha, beta )

Returns the differential entropy of a Pareto (Type I) distribution with parameters shape parameter alpha and scale parameter beta (in nats).

var v = entropy( 2.0, 1.0 );
// returns ~0.807

v = entropy( 4.0, 12.0 );
// returns ~2.349

v = entropy( 8.0, 2.0 );
// returns ~-0.261


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 alpha <= 0, the function returns NaN.

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

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


If provided beta <= 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/pareto-type1/entropy' );

var alpha;
var beta;
var v;
var i;

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