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

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# Entropy

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> [Arcsine][arcsine-distribution] distribution [differential entropy][entropy].

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<section class="intro">

The [differential entropy][entropy] (in [nats][nats]) for an [arcsine][arcsine-distribution] random variable with minimum support `a` and maximum support `b` is

<!-- <equation class="equation" label="eq:arcsine_entropy" align="center" raw="h\left( X \right) = \ln {\tfrac{\pi}{4}}" alt="Differential entropy for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="h\left( X \right) = \ln {\tfrac{\pi}{4}}" data-equation="eq:arcsine_entropy">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/entropy/docs/img/equation_arcsine_entropy.svg" alt="Differential entropy for an arcsine distribution.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### entropy( a, b )

Returns the [differential entropy][entropy] of an [arcsine][arcsine-distribution] distribution with minimum support `a` and maximum support `b` (in [nats][nats]).

```javascript
var v = entropy( 0.0, 1.0 );
// returns ~-0.242

v = entropy( 4.0, 12.0 );
// returns ~1.838

v = entropy( 2.0, 8.0 );
// returns ~1.55
```

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 `a >= b`, the function returns `NaN`.

```javascript
var y = entropy( 3.0, 2.0 );
// returns NaN

y = entropy( 3.0, 3.0 );
// 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 logEachMap = require( '@stdlib/console-log-each-map' );
var entropy = require( '@stdlib/stats-base-dists-arcsine-entropy' );

var opts = {
    'dtype': 'float64'
};
var a = uniform( 25, 0.0, 10.0, opts );
var b = uniform( a.length, 15.0, 25.0, opts );

logEachMap( 'a: %0.4f, b: %0.4f, h(X;a,b): %0.4f', a, b, 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/arcsine/entropy.h"
```

#### stdlib_base_dists_arcsine_entropy( a, b )

Returns the differential entropy of an arcsine distribution.

```c
double out = stdlib_base_dists_arcsine_entropy( -4.0, 4.0 );
// returns ~1.838
```

The function accepts the following arguments:

-   **a**: `[in] double` minimum support.
-   **b**: `[in] double` maximum support.

```c
double stdlib_base_dists_arcsine_entropy( const double a, const double b );
```

</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/arcsine/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 a;
    double b;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        a = random_uniform( 0.0, 20.0 );
        b = random_uniform( a, a+20.0 );
        y = stdlib_base_dists_arcsine_entropy( a, b );
        printf( "x: %lf, a: %lf, b: %lf, h(X;a,b): %lf\n", a, b, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="references">

</section>

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</section>

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<section class="main-repo" >

* * *

## 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

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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-arcsine-entropy/main/LICENSE

[arcsine-distribution]: https://en.wikipedia.org/wiki/Arcsine_distribution

[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[nats]: https://en.wikipedia.org/wiki/Nat_%28unit%29

</section>

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