@stdlib/stats/base/dists/studentized-range/cdf/README.md

Standard library statistical functions.

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# Cumulative Distribution Function

> [Studentized range][studentized-range] distribution [cumulative distribution function][cdf] (CDF).

<section class="intro">

</section>

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<section class="usage">

## Usage

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

#### cdf( x, r, v\[, nranges=1] )

Evaluates the [cumulative distribution function][cdf] (CDF) for a [studentized range][studentized-range] distribution with sample size `r` and `v` degrees of freedom. Optionally, the number of groups whose maximum range is considered can be specified via the `nranges` parameter.

```javascript
var y = cdf( 0.5, 3.0, 2.0 );
// returns ~0.0644

y = cdf( 12.1, 17.0, 2.0 );
// returns ~0.913

y = cdf( 0.5, 3.0, 2.0, 2 );
// returns ~0.01
```

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

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

y = cdf( 1.5, NaN, 2.0 );
// returns NaN
```

If provided `v < 2` or `r < 2`, the function returns `NaN`.

```javascript
var y = cdf( 2.0, -1.0, 3.0 );
// returns NaN

y = cdf( 2.0, 3.0, 1.5 );
// returns NaN
```

#### cdf.factory( r, v\[, nranges=1] )

Returns a `function` for evaluating the [cdf][cdf] of a [studentized range][studentized-range] distribution with sample size `r` and `v` degrees of freedom. Optionally. Optionally, the number of groups whose maximum range is considered can be specified via the `nranges` parameter.

```javascript
var mycdf = cdf.factory( 3.0, 2.0 );
var y = mycdf( 3.0 );
// returns ~0.712

y = mycdf( 1.0 );
// returns ~0.216
```

</section>

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<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var cdf = require( '@stdlib/stats/base/dists/studentized-range/cdf' );

var v;
var q;
var r;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    q = randu() * 12.0;
    r = ( randu() * 20.0 ) + 2.0;
    v = ( randu() * 10.0 ) + 2.0;
    y = cdf( q, r, v );
    console.log( 'q: %d, r: %d, v: %d, F(x;v): %d', q.toFixed( 4 ), r.toFixed( 4 ), v.toFixed( 4 ), y.toFixed( 4 ) );
}
```

</section>

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<section class="related">

</section>

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<section class="links">

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

[studentized-range]: https://en.wikipedia.org/wiki/Studentized_range_distribution

</section>

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