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

Standard library statistical functions.

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# Cumulative Distribution Function

> [Chi-squared][chisquare-distribution] distribution [cumulative distribution function][cdf].

<section class="intro">

The [cumulative distribution function][cdf] for a [chi-squared][chisquare-distribution] random variable is

<!-- <equation class="equation" label="eq:chisquare_cdf" align="center" raw="F(x;\,k) = P\left(\frac{x}{2},\,\frac{k}{2}\right)" alt="Cumulative distribution function for a chi-squared distribution."> -->

<div class="equation" align="center" data-raw-text="F(x;\,k) = P\left(\frac{x}{2},\,\frac{k}{2}\right)" data-equation="eq:chisquare_cdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/chisquare/cdf/docs/img/equation_chisquare_cdf.svg" alt="Cumulative distribution function for a chi-squared distribution.">
    <br>
</div>

<!-- </equation> -->

where `k` is the degrees of freedom and `P` is the lower regularized incomplete gamma function.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### cdf( x, k )

Evaluates the [cumulative distribution function][cdf] (CDF) for a [chi-squared][chisquare-distribution] distribution with degrees of freedom `k`.

```javascript
var y = cdf( 2.0, 1.0 );
// returns ~0.843

y = cdf( 2.0, 3.0 );
// returns ~0.428

y = cdf( 1.0, 0.5 );
// returns ~0.846

y = cdf( -1.0, 2.0 );
// returns 0.0

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

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

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

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

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

If provided `k < 0`, the function returns `NaN`.

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

If provided `k = 0`, the function evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at `0`.

```javascript
var y = cdf( 2.0, 0.0 );
// returns 1.0

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

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

#### cdf.factory( k )

Returns a function for evaluating the [cumulative distribution function][cdf] for a [chi-squared][chisquare-distribution] distribution with degrees of freedom `k`.

```javascript
var mycdf = cdf.factory( 3.0 );

var y = mycdf( 6.0 );
// returns ~0.888

y = mycdf( 1.5 );
// returns ~0.318
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var cdf = require( '@stdlib/stats/base/dists/chisquare/cdf' );

var k;
var x;
var y;
var i;

for ( i = 0; i < 20; i++ ) {
    x = randu() * 10.0;
    k = round( randu()*5.0 );
    y = cdf( x, k );
    console.log( 'x: %d, k: %d, F(x;k): %d', x.toFixed( 4 ), k.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">

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

[chisquare-distribution]: https://en.wikipedia.org/wiki/Chi-squared_distribution

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution

</section>

<!-- /.links -->