Entropy

Chi distribution differential entropy.

The differential entropy (in nats) for a chi random variable is

where k > 0 is the degrees of freedom and Γ and Ψ denote the gamma and digamma functions, respectively.

Installation

npm install @stdlib/stats-base-dists-chi-entropy

Usage

var entropy = require( '@stdlib/stats-base-dists-chi-entropy' );

entropy( k )

Returns the differential entropy of a chi distribution with degrees of freedom k (in nats).

var v = entropy( 9.0 );
// returns ~1.052

v = entropy( 0.5 );
// returns ~0.135

If provided k <= 0, the function returns NaN.

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

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var entropy = require( '@stdlib/stats-base-dists-chi-entropy' );

var opts = {
    'dtype': 'float64'
};
var k = uniform( 10, 0.0, 20.0, opts );

logEachMap( 'k: %0.4f, h(X;k): %0.4f', k, entropy );

C APIs

Usage

#include "stdlib/stats/base/dists/chi/entropy.h"

stdlib_base_dists_chi_entropy( k )

Returns the differential entropy of a chi distribution with degrees of freedom k (in nats).

double out = stdlib_base_dists_chi_entropy( 9.0 );
// returns ~1.052

The function accepts the following arguments:

• k: [in] double degrees of freedom (must be positive).

double stdlib_base_dists_chi_entropy( const double k );

Examples

#include "stdlib/stats/base/dists/chi/entropy.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v * ( max - min ) );
}

int main( void ) {
    double result;
    double k;
    int i;

    for ( i = 0; i < 10; i++ ) {
        k = random_uniform( 0.0, 10.0 );
        result = stdlib_base_dists_chi_entropy( k );
        printf( "k: %lf, h(X,k): %lf \n", k, result );
    }
}

Notice

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.