Entropy

Triangular distribution differential entropy.

The differential entropy (in nats) for a triangular random variable with lower limit a, upper limit b, and mode c is

h left-parenthesis upper X right-parenthesis equals one-half plus ln left-parenthesis StartFraction b minus a Over 2 EndFraction right-parenthesis

Usage

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

entropy( a, b, c )

Returns the differential entropy of a triangular distribution with minimum support a, maximum supportb, and mode c (in nats).

var v = entropy( 0.0, 1.0, 0.8 );
// returns ~-0.193

v = entropy( 4.0, 12.0, 5.0 );
// returns ~1.886

v = entropy( 2.0, 8.0, 5.0 );
// returns ~1.599

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

var v = entropy( NaN, 4.0, 2.0 );
// returns NaN

v = entropy( 0.0, NaN, 2.0 );
// returns NaN

v = entropy( 0.0, 4.0, NaN );
// returns NaN

If provided parameters not satisfying a <= c <= b, the function returns NaN.

var y = entropy( 1.0, 0.0, 1.5 );
// returns NaN

y = entropy( 0.0, 1.0, -1.0 );
// returns NaN

y = entropy( 0.0, -1.0, 0.5 );
// returns NaN

Examples

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

var a;
var b;
var c;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = ( randu()*10.0 );
    b = ( randu()*10.0 ) + a;
    c = ( randu()*( b-a ) ) + a;
    v = entropy( a, b, c );
    console.log( 'a: %d, b: %d, c: %d, h(X;a,b,c): %d', a.toFixed( 4 ), b.toFixed( 4 ), c.toFixed( 4 ), v.toFixed( 4 ) );
}