npm package: @stdlib/stats-base-dists-erlang-entropy
Description: Erlang distribution differential entropy.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Entropy

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> [Erlang][erlang-distribution] distribution [differential entropy][entropy].

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

The [differential entropy][entropy] for an [Erlang][erlang-distribution] random variable with shape `k` and rate `λ` is

<!-- <equation class="equation" label="eq:erlang_entropy" align="center" raw="h\left( X \right) = (1\,-\,k)\psi (k)\,+\,\ln \left[{\frac {\Gamma (k)}{\lambda }}\right]\,+\,k" alt="Differential entropy for an Erlang distribution."> -->

<div class="equation" align="center" data-raw-text="h\left( X \right) = (1\,-\,k)\psi (k)\,+\,\ln \left[{\frac {\Gamma (k)}{\lambda }}\right]\,+\,k" data-equation="eq:erlang_entropy">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/erlang/entropy/docs/img/equation_erlang_entropy.svg" alt="Differential entropy for an Erlang distribution.">
    <br>
</div>

<!-- </equation> -->

where `Γ` and `Ψ` denote the [gamma][gamma-function] and [digamma][digamma] function, respectively.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-erlang-entropy
```

</section>

<section class="usage">

## Usage

```javascript
var entropy = require( '@stdlib/stats-base-dists-erlang-entropy' );
```

#### entropy( k, lambda )

Returns the [differential entropy][entropy] of an [Erlang][erlang-distribution] distribution with parameters shape `k` and rate `lambda` (in [nats][nats]).

```javascript
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`.

```javascript
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`.

```javascript
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`.

```javascript
var v = entropy( 2, 0.0 );
// returns NaN

v = entropy( 2, -1.0 );
// returns NaN
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var entropy = require( '@stdlib/stats-base-dists-erlang-entropy' );

var opts = {
    'dtype': 'float64'
};
var k = discreteUniform( 10, 0, 10, opts );
var lambda = uniform( 10, EPS, 10.0, opts );

logEachMap( 'k: %d, λ: %0.4f, h(X;k,λ): %0.4f', k, lambda, entropy );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/base/dists/erlang/entropy.h"
```

#### stdlib_base_dists_erlang_entropy( k, lambda )

Returns the [differential entropy][entropy] of an [Erlang][erlang-distribution] distribution with parameters shape `k` and rate `lambda` (in [nats][nats]).

```c
double y = stdlib_base_dists_erlang_entropy( 1, 1.0 );
// returns 1.0
```

The function accepts the following arguments:

-   **k**: `[in] int32_t` shape parameter.
-   **lambda**: `[in] double` rate parameter.

```c
double stdlib_base_dists_erlang_entropy( const int32_t k, const double lambda );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section`
element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/erlang/entropy.h"
#include "stdlib/constants/float64/eps.h"
#include "stdlib/math/base/special/round.h"
#include <stdint.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 lambda;
    int32_t k;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        k = stdlib_base_round( random_uniform( 0.0, 10.0 ) );
        lambda = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        y = stdlib_base_dists_erlang_entropy( k, lambda );
        printf( "k: %d, λ: %lf, h(X;k,λ): %lf\n", k, lambda, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="references">

</section>

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<section class="related">

</section>

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* * *

## 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].

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## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-erlang-entropy/main/LICENSE

[erlang-distribution]: https://en.wikipedia.org/wiki/Erlang_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

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