Erlang distribution differential entropy.
APACHE-2.0 License
Erlang distribution differential entropy.
The differential entropy for an Erlang random variable with shape k
and rate λ
is
h\left( X \right) = (1\,-\,k)\psi (k)\,+\,\ln \left[{\frac {\Gamma (k)}{\lambda }}\right]\,+\,k
where Γ
and Ψ
denote the gamma and digamma function, respectively.
npm install @stdlib/stats-base-dists-erlang-entropy
Alternatively,
script
tag without installation and bundlers, use the ES Module available on the esm
branch (see README).deno
branch (see README for usage intructions).umd
branch (see README).The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
var entropy = require( '@stdlib/stats-base-dists-erlang-entropy' );
Returns the differential entropy of an Erlang distribution with parameters shape k
and rate lambda
(in nats).
var v = entropy( 1, 1.0 );
// returns 1.0
v = entropy( 4, 12.0 );
// returns ~-0.462
v = entropy( 8, 2.0 );
// returns ~1.723
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 not provided a positive integer for k
, the function returns NaN
.
var v = entropy( 1.8, 1.0 );
// returns NaN
v = entropy( -1.0, 1.0 );
// returns NaN
If provided lambda <= 0
, the function returns NaN
.
var v = entropy( 2, 0.0 );
// returns NaN
v = entropy( 2, -1.0 );
// returns NaN
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var EPS = require( '@stdlib/constants-float64-eps' );
var entropy = require( '@stdlib/stats-base-dists-erlang-entropy' );
var lambda;
var k;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
k = round( randu()*10.0 );
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 ) );
}
This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.
See LICENSE.
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