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

Standard library statistical functions.

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# Cumulative Distribution Function

> [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution [cumulative distribution function][cdf].

<section class="intro">

The [cumulative distribution function][cdf] for a [Kumaraswamy's double bounded][kumaraswamy-distribution] random variable is

<!-- <equation class="equation" label="eq:kumaraswamy_cdf" align="center" raw="F(x;a,b) = 1-(1-x^{a})^{b}" alt="Cumulative distribution function for a Kumaraswamy's double bounded distribution."> -->

<div class="equation" align="center" data-raw-text="F(x;a,b) = 1-(1-x^{a})^{b}" data-equation="eq:kumaraswamy_cdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/cdf/docs/img/equation_kumaraswamy_cdf.svg" alt="Cumulative distribution function for a Kumaraswamy's double bounded distribution.">
    <br>
</div>

<!-- </equation> -->

where `a > 0` is the first shape parameter and `b > 0` is the second shape parameter.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### cdf( x, a, b )

Evaluates the [cumulative distribution function][cdf] (CDF) for a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with parameters `a` (first shape parameter) and `b` (second shape parameter).

```javascript
var y = cdf( 0.5, 1.0, 1.0 );
// returns 0.5

y = cdf( 0.5, 2.0, 4.0 );
// returns ~0.684

y = cdf( 0.2, 2.0, 2.0 );
// returns ~0.078

y = cdf( 0.8, 4.0, 4.0 );
// returns ~0.878

y = cdf( -0.5, 4.0, 2.0 );
// returns 0.0

y = cdf( -Infinity, 4.0, 2.0 );
// returns 0.0

y = cdf( 1.5, 4.0, 2.0 );
// returns 1.0

y = cdf( +Infinity, 4.0, 2.0 );
// returns 1.0
```

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

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

y = cdf( 0.0, NaN, 1.0 );
// returns NaN

y = cdf( 0.0, 1.0, NaN );
// returns NaN
```

If provided `a <= 0`, the function returns `NaN`.

```javascript
var y = cdf( 2.0, -1.0, 0.5 );
// returns NaN

y = cdf( 2.0, 0.0, 0.5 );
// returns NaN
```

If provided `b <= 0`, the function returns `NaN`.

```javascript
var y = cdf( 2.0, 0.5, -1.0 );
// returns NaN

y = cdf( 2.0, 0.5, 0.0 );
// returns NaN
```

#### cdf.factory( a, b )

Returns a function for evaluating the [cumulative distribution function][cdf] for a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with parameters `a` (first shape parameter) and `b` (second shape parameter).

```javascript
var mycdf = cdf.factory( 0.5, 0.5 );

var y = mycdf( 0.8 );
// returns ~0.675

y = mycdf( 0.3 );
// returns ~0.327
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var cdf = require( '@stdlib/stats/base/dists/kumaraswamy/cdf' );

var a;
var b;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu();
    a = ( randu()*5.0 ) + EPS;
    b = ( randu()*5.0 ) + EPS;
    y = cdf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, F(x;a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

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

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

</section>

<!-- /.links -->