Probability Density Function

Gamma distribution probability density function (PDF).

The probability density function (PDF) for a gamma random variable is

where α > 0 is the shape parameter and β > 0 is the rate parameter.

Installation

npm install @stdlib/stats-base-dists-gamma-pdf

Usage

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

pdf( x, alpha, beta )

Evaluates the probability density function (PDF) for a gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var y = pdf( 2.0, 0.5, 1.0 );
// returns ~0.054

y = pdf( 0.1, 1.0, 1.0 );
// returns ~0.905

y = pdf( -1.0, 4.0, 2.0 );
// returns 0.0

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

var y = pdf( NaN, 1.0, 1.0 );
// returns NaN

y = pdf( 0.0, NaN, 1.0 );
// returns NaN

y = pdf( 0.0, 1.0, NaN );
// returns NaN

If provided alpha < 0, the function returns NaN.

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

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

var y = pdf( 2.0, 0.0, 2.0 );
// returns 0.0

y = pdf( 0.0, 0.0, 2.0 );
// returns Infinity

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

var y = pdf( 2.0, 1.0, 0.0 );
// returns NaN

y = pdf( 2.0, 1.0, -1.0 );
// returns NaN

pdf.factory( alpha, beta )

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

var mypdf = pdf.factory( 3.0, 1.5 );

var y = mypdf( 1.0 );
// returns ~0.377

y = mypdf( 4.0 );
// returns ~0.067

Examples

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

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 = pdf( 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.

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Copyright

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