npm package: @stdlib/stats-base-dists-studentized-range-cdf
Description: Studentized range cumulative distribution function (CDF).
Author: The Stdlib Authors
Latest version: 0.2.3

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  <summary>
    About stdlib...
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# Cumulative Distribution Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

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

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-studentized-range-cdf
```

</section>

<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, 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>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-studentized-range-cdf' );

var opts = {
    'dtype': 'float64'
};
var q = uniform( 10, 0.0, 12.0, opts );
var r = uniform( 10, 2.0, 20.0, opts );
var v = uniform( 10, 2.0, 10.0, opts );

logEachMap( 'q: %0.4f, r: %0.4f, v: %0.4f, F(x;v): %0.4f', q, r, v, cdf );
```

</section>

<!-- /.examples -->

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<section class="related">

</section>

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-studentized-range-cdf/main/LICENSE

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

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

</section>

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