@stdlib/stats-base-dists-frechet-entropy
v0.3.1TypeScript
Fréchet distribution differential entropy.
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Published by The Stdlib Authors
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About stdlib...
Entropy
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> [Fréchet][frechet-distribution] distribution [differential entropy][entropy].
The [differential entropy][entropy] for a [Fréchet][frechet-distribution] random variable shape α > 0, scale s > 0, and location parameter m is
where γ is the [Euler–Mascheroni constant][euler-mascheroni].
Installation
``bash`
npm install @stdlib/stats-base-dists-frechet-entropy
Usage
`javascript`
var entropy = require( '@stdlib/stats-base-dists-frechet-entropy' );
#### entropy( alpha, s, m )
Returns the [differential entropy][entropy] for a [Fréchet][frechet-distribution] distribution with shape alpha > 0, scale s > 0, and location parameter m (in [nats][nats]).
`javascript
var y = entropy( 2.0, 1.0, 1.0 );
// returns ~1.173
y = entropy( 1.0, 1.0, -1.0 );
// returns ~2.154
y = entropy( 1.0, 1.0, 2.0 );
// returns ~2.154
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = entropy( NaN, 1.0, -2.0 );
// returns NaN
y = entropy( 1.0, NaN, -2.0 );
// returns NaN
y = entropy( 1.0, 1.0, NaN );
// returns NaN
`
If provided alpha <= 0, the function returns NaN.
`javascript
var y = entropy( 0.0, 3.0, 2.0 );
// returns NaN
y = entropy( 0.0, -1.0, 2.0 );
// returns NaN
`
If provided s <= 0, the function returns NaN.
`javascript
var y = entropy( 1.0, 0.0, 2.0 );
// returns NaN
y = entropy( 1.0, -1.0, 2.0 );
// returns NaN
`
Examples
`javascript
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var entropy = require( '@stdlib/stats-base-dists-frechet-entropy' );
var alpha;
var m;
var s;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
alpha = ( randu()*20.0 ) + EPS;
s = ( randu()*20.0 ) + EPS;
m = ( randu()*40.0 ) - 20.0;
y = entropy( alpha, s, m );
console.log( 'α: %d, s: %d, m: %d, h(X;α,s,m): %d', alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/frechet/entropy.h"
#### stdlib_base_dists_frechet_entropy( alpha, s, m )
Returns the differential entropy for a Fréchet distribution with shape alpha, scale s, and location m.
`c`
double y = stdlib_base_dists_frechet_entropy( 5.0, 2.0, 0.0 );
// returns ~0.776
The function accepts the following arguments:
- alpha: [in] double shape parameter.[in] double
- s: scale parameter.[in] double
- m: location parameter.
`c`
double stdlib_base_dists_frechet_entropy( const double alpha, const double s, const double m );
$3
`c
#include "stdlib/stats/base/dists/frechet/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 s;
double m;
double y;
int i;
for ( i = 0; i < 10; i++ ) {
alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
s = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
m = random_uniform( -20.0, 20.0 );
y = stdlib_base_dists_frechet_entropy( alpha, s, m );
printf( "α: %.4lf, s: %.4lf, m: %.4lf, h(X;α,s,m): %.4lf\n", alpha, s, m, 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-frechet-entropy/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-frechet-entropy/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-frechet-entropy/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-frechet-entropy/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-frechet-entropy/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-frechet-entropy/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-frechet-entropy/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-frechet-entropy/main/LICENSE
[euler-mascheroni]: https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant
[frechet-distribution]: https://en.wikipedia.org/wiki/Fr%C3%A9chet_distribution
[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29
[nats]: https://en.wikipedia.org/wiki/Nat_%28unit%29