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# npm

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

0.0.7 • Public • Published

# Cumulative Distribution Function

Gamma distribution cumulative distribution function.

The cumulative distribution function for a gamma random variable is

where `alpha` is the shape parameter and `beta` is the rate parameter of the distribution. `gamma` is the lower incomplete gamma function.

## Installation

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

## Usage

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

#### cdf( x, alpha, beta )

Evaluates the cumulative distribution function (CDF) for a gamma distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).

```var y = cdf( 2.0, 1.0, 1.0 );
// returns ~0.865

y = cdf( 2.0, 3.0, 1.0 );
// returns ~0.323

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

y = cdf( -Infinity, 4.0, 2.0 );
// 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 `alpha < 0`, the function returns `NaN`.

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

If provided `alpha = 0`, the function evaluates the CDF of a degenerate distribution centered at `0`.

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

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

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

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

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

#### cdf.factory( alpha, beta )

Returns a function for evaluating the cumulative distribution function for a gamma distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).

```var mycdf = cdf.factory( 0.5, 0.1 );

var y = mycdf( 12.0 );
// returns ~0.879

y = mycdf( 8.0 );
// returns ~0.794```

## Examples

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

var alpha;
var beta;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
x = randu() * 3.0;
alpha = randu() * 5.0;
beta = randu() * 5.0;
y = cdf( x, alpha, beta );
console.log( 'x: %d, α: %d, β: %d, F(x;α,β): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.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-gamma-cdf`

stdlib.io

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