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# Entropy

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

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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.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/stats/base/dists/triangular/entropy/docs/img/equation_triangular_entropy.svg" alt="Differential entropy for a triangular distribution.">
    <br>
</div>

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</section>

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<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>

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</section>

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<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>

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<section class="references">

</section>

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<section class="links">

[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

</section>

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