npm package: @stdlib/stats-base-dists-triangular-entropy
Description: Triangular 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] -->

> [Triangular][triangular-distribution] distribution [differential entropy][entropy].

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<section class="intro">

The [differential entropy][entropy] (in [nats][nats]) for a [triangular][triangular-distribution] random variable with lower limit `a`, upper limit `b`, and mode `c` is

<!-- <equation class="equation" label="eq:triangular_entropy" align="center" raw="h\left( X \right) = \frac{1}{2} + \ln \left({\frac{b-a}{2}}\right)" alt="Differential entropy for a triangular distribution."> -->

<div class="equation" align="center" data-raw-text="h\left( X \right) = \frac{1}{2} + \ln \left({\frac{b-a}{2}}\right)" data-equation="eq:triangular_entropy">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@556e0ebc42f54244079cecc91c0883bb6c442244/lib/node_modules/@stdlib/stats/base/dists/triangular/entropy/docs/img/equation_triangular_entropy.svg" alt="Differential entropy for a triangular distribution.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### entropy( a, b, c )

Returns the [differential entropy][entropy] of a [triangular][triangular-distribution] distribution with minimum support `a`, maximum support`b`, and mode `c` (in [nats][nats]).

```javascript
var v = entropy( 0.0, 1.0, 0.8 );
// returns ~-0.193

v = entropy( 4.0, 12.0, 5.0 );
// returns ~1.886

v = entropy( 2.0, 8.0, 5.0 );
// returns ~1.599
```

If provided `NaN` as any argument, the function returns `NaN`.

```javascript
var v = entropy( NaN, 4.0, 2.0 );
// returns NaN

v = entropy( 0.0, NaN, 2.0 );
// returns NaN

v = entropy( 0.0, 4.0, NaN );
// returns NaN
```

If provided parameters not satisfying `a <= c <= b`, the function returns `NaN`.

```javascript
var y = entropy( 1.0, 0.0, 1.5 );
// returns NaN

y = entropy( 0.0, 1.0, -1.0 );
// returns NaN

y = entropy( 0.0, -1.0, 0.5 );
// returns NaN
```

</section>

<!-- /.usage -->

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<section class="notes">

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

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

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

var a;
var b;
var c;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = ( randu()*10.0 );
    b = ( randu()*10.0 ) + a;
    c = ( randu()*( b-a ) ) + a;
    v = entropy( a, b, c );
    console.log( 'a: %d, b: %d, c: %d, h(X;a,b,c): %d', a.toFixed( 4 ), b.toFixed( 4 ), c.toFixed( 4 ), v.toFixed( 4 ) );
}
```

</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/triangular/entropy.h"
```

#### stdlib_base_dists_triangular_entropy( a, b, c )

Returns the [differential entropy][entropy] of a [triangular][triangular-distribution] distribution with minimum support `a`, maximum support`b`, and mode `c` (in [nats][nats]).

```c
double out = stdlib_base_dists_triangular_entropy( 0.0, 1.0, 0.5 );
// returns ~-0.193
```

The function accepts the following arguments:

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

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

</section>

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<section class="notes">

</section>

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

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/triangular/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 c;
    double v;
    int i;

    for ( i = 0; i < 25; i++ ) {
        a = random_uniform( 0.0, 10.0 );
        b = random_uniform( a, a+10.0 );
        c = random_uniform( a, b );
        v = stdlib_base_dists_triangular_entropy( a, b, c );
        printf( "a: %lf, b: %lf, c: %lf, h(X;a,b,c): %lf\n", a, b, c, v );
    }
}
```

</section>

<!-- /.examples -->

</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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[triangular-distribution]: https://en.wikipedia.org/wiki/Triangular_distribution

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

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

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