Nasty Pirate Macaw

# npm

## @stdlib/stats-base-dists-f-cdf

0.0.6 • Public • Published

# Cumulative Distribution Function

F distribution cumulative distribution function.

The cumulative distribution function for a F random variable is

where `d1` is the numerator degrees of freedom, `d2` is the denominator degrees of freedom and `I_{x}(a,b)` is the lower regularized incomplete beta function.

## Installation

`npm install @stdlib/stats-base-dists-f-cdf`

## Usage

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

#### cdf( x, d1, d2 )

Evaluates the cumulative distribution function (CDF) for a F distribution with parameters `d1` (numerator degrees of freedom) and `d2` (denominator degrees of freedom).

```var y = cdf( 2.0, 1.0, 1.0 );
// returns ~0.608

y = cdf( 2.0, 8.0, 4.0 );
// returns ~0.737

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

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

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

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

```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 `d1 <= 0`, the function returns `NaN`.

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

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

If provided `d2 <= 0`, the function returns `NaN`.

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

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

#### cdf.factory( d1, d2 )

Returns a function for evaluating the cumulative distribution function of a F distribution with parameters `d1` (numerator degrees of freedom) and `d2` (denominator degrees of freedom).

```var mycdf = cdf.factory( 10.0, 2.0 );

var y = mycdf( 10.0 );
// returns ~0.906

y = mycdf( 8.0 );
// returns ~0.884```

## Examples

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

var d1;
var d2;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
x = randu() * 10.0;
d1 = randu() * 10.0;
d2 = randu() * 10.0;
y = cdf( x, d1, d2 );
console.log( 'x: %d, d1: %d, d2: %d, F(x;d1,d2): %d', x.toFixed( 4 ), d1.toFixed( 4 ), d2.toFixed( 4 ), y.toFixed( 4 ) );
}```

## Notice

This package is part of 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, see the main project repository.

### Install

`npm i @stdlib/stats-base-dists-f-cdf`

### Repository

github.com/stdlib-js/stats-base-dists-f-cdf

stdlib.io

147

0.0.6

Apache-2.0

57 kB

11