@stdlib/stats-base-dists-gamma-cdf
v0.2.2
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Gamma distribution cumulative distribution function (CDF).
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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.
Community
License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.