@stdlib/stats/base/dists/kumaraswamy/mode/README.md

Standard library statistical functions.

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# Mode

> [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution [mode][mode].

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The [mode][mode] for a [Kumaraswamy's double bounded][kumaraswamy-distribution] random variable with first shape parameter `a` and second shape parameter `b` is

<!-- <equation class="equation" label="eq:kumaraswamy_mode" align="center" raw="\operatorname{mode}\left( X \right) = \left(\frac{a-1}{ab-1}\right)^{1/a}" alt="Mode for a Kumaraswamy's double bounded distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{mode}\left( X \right) = \left(\frac{a-1}{ab-1}\right)^{1/a}" data-equation="eq:kumaraswamy_mode">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/mode/docs/img/equation_kumaraswamy_mode.svg" alt="Mode for a Kumaraswamy's double bounded distribution.">
    <br>
</div>

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for `a >= 1`, `b >=1` and not `a = b = 1`.

</section>

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<section class="usage">

## Usage

```javascript
var mode = require( '@stdlib/stats/base/dists/kumaraswamy/mode' );
```

#### mode( a, b )

Returns the [mode][mode] of a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with first shape parameter `a` and second shape parameter `b`.

```javascript
var v = mode( 1.5, 1.5 );
// returns ~0.543

v = mode( 4.0, 12.0 );
// returns ~0.503

v = mode( 2.0, 8.0 );
// returns ~0.258
```

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

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

v = mode( 2.0, NaN );
// returns NaN
```

If provided `a = 1` and `b = 1`, the function returns `NaN`.

```javascript
var y = mode( 1.0, 1.0 );
// returns NaN
```

If provided `a < 1`, the function returns `NaN`.

```javascript
var y = mode( -1.0, 2.0 );
// returns NaN

y = mode( 0.0, 2.0 );
// returns NaN
```

If provided `b < 1`, the function returns `NaN`.

```javascript
var y = mode( 2.0, -1.0 );
// returns NaN

y = mode( 2.0, 0.0 );
// returns NaN
```

</section>

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</section>

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## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var mode = require( '@stdlib/stats/base/dists/kumaraswamy/mode' );

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

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

</section>

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</section>

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</section>

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<section class="links">

[kumaraswamy-distribution]: https://en.wikipedia.org/wiki/Kumaraswamy_distribution

[mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29

</section>

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