Pareto (Type I) distribution differential entropy.
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[Pareto (Type I)][pareto-distribution] distribution [differential entropy][entropy].
math
h\left( X \right) = \ln\left(\left({\frac{\beta}{\alpha}}\right) \, e^{1+{\tfrac{1}{\alpha }}}\right)α > 0 is the shape parameter and β > 0 is the scale parameter.bash
npm install @stdlib/stats-base-dists-pareto-type1-entropyscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var entropy = require( '@stdlib/stats-base-dists-pareto-type1-entropy' );alpha and scale parameter beta (in [nats][nats]).javascript
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 ~-0.261NaN as any argument, the function returns NaN.javascript
var v = entropy( NaN, 2.0 );
// returns NaN
v = entropy( 2.0, NaN );
// returns NaNalpha <= 0, the function returns NaN.javascript
var v = entropy( 0.0, 1.0 );
// returns NaN
v = entropy( -1.0, 1.0 );
// returns NaNbeta <= 0, the function returns NaN.javascript
var v = entropy( 1.0, 0.0 );
// returns NaN
v = entropy( 1.0, -1.0 );
// returns NaNjavascript
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var entropy = require( '@stdlib/stats-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 ) );
}
