@stdlib/stats-base-dists-gamma-entropy
v0.3.1TypeScript
Gamma distribution differential entropy.
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Published by The Stdlib Authors
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About stdlib...
Entropy
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> [Gamma][gamma-distribution] distribution [differential entropy][entropy].
The [differential entropy][entropy] (in [nats][nats]) for a [gamma][gamma-distribution] random variable with shape parameter α > 0 and rate parameter β > 0 is
where Γ and Ψ denote the [gamma][gamma-function] and [digamma][digamma] function, respectively.
Installation
``bash`
npm install @stdlib/stats-base-dists-gamma-entropy
Usage
`javascript`
var entropy = require( '@stdlib/stats-base-dists-gamma-entropy' );
#### entropy( alpha, beta )
Returns the [differential entropy][entropy] of a [gamma][gamma-distribution] distribution with shape parameter alpha and rate parameter beta (in [nats][nats]).
`javascript
var v = entropy( 1.0, 1.0 );
// returns 1.0
v = entropy( 4.0, 12.0 );
// returns ~-0.462
v = entropy( 8.0, 2.0 );
// returns ~1.723
`
If provided NaN as any argument, the function returns NaN.
`javascript
var v = entropy( NaN, 2.0 );
// returns NaN
v = entropy( 2.0, NaN );
// returns NaN
`
If provided alpha <= 0, the function returns NaN.
`javascript
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.
`javascript
var v = entropy( 1.0, 0.0 );
// returns NaN
v = entropy( 1.0, -1.0 );
// returns NaN
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var entropy = require( '@stdlib/stats-base-dists-gamma-entropy' );
var opts = {
'dtype': 'float64'
};
var alpha = uniform( 10, EPS, 10.0, opts );
var beta = uniform( 10, EPS, 10.0, opts );
logEachMap( 'α: %0.4f, β: %0.4f, h(X;α,β): %0.4f', alpha, beta, entropy );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/gamma/entropy.h"
#### stdlib_base_dists_gamma_entropy( alpha, beta )
Returns the differential entropy of a gamma distribution with shape parameter alpha and rate parameter beta.
`c`
double y = stdlib_base_dists_gamma_entropy( 1.0, 1.0 );
// returns 1.0
The function accepts the following arguments:
- alpha: [in] double shape parameter.[in] double
- beta: rate parameter.
`c`
double stdlib_base_dists_gamma_entropy( const double alpha, const double beta );
$3
`c
#include "stdlib/stats/base/dists/gamma/entropy.h"
#include "stdlib/constants/float64/eps.h"
#include
#include
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 alpha;
double beta;
double y;
int i;
for ( i = 0; i < 10; i++ ) {
alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
beta = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 ) ;
y = stdlib_base_dists_gamma_entropy( alpha, beta );
printf( "α: %1f, β: %1f, h(X;α,β): %lf\n", alpha, beta, y );
}
}
`
*
Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[stdlib]: https://github.com/stdlib-js/stdlib
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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-gamma-entropy/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-entropy/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-gamma-entropy/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-entropy/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-gamma-entropy/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-entropy/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-gamma-entropy/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-gamma-entropy/main/LICENSE
[gamma-distribution]: https://en.wikipedia.org/wiki/Gamma_distribution
[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29
[nats]: https://en.wikipedia.org/wiki/Nat_%28unit%29
[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
[digamma]: https://en.wikipedia.org/wiki/Digamma_function