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 uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var pdf = require( '@stdlib/stats-base-dists-gamma-pdf' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 10, 0.0, 3.0, opts );
var alpha = uniform( 10, EPS, 5.0, opts );
var beta = uniform( 10, EPS, 5.0, opts );

logEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, f(x;α,β): %0.4f', x, alpha, beta, pdf );

C APIs

Usage

#include "stdlib/stats/base/dists/gamma/pdf.h"

stdlib_base_dists_gamma_pdf( x, alpha, beta )

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

double y = stdlib_base_dists_gamma_pdf( 2.0, 0.5, 1.0 );
// returns ~0.054

The function accepts the following arguments:

• x: [in] double input value.
• alpha: [in] double shape parameter.
• beta: [in] double rate parameter.

double stdlib_base_dists_gamma_pdf( const double x, const double alpha, const double beta );

Examples

#include "stdlib/stats/base/dists/gamma/pdf.h"
#include "stdlib/constants/float64/eps.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double alpha;
    double beta;
    double x;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = random_uniform( 0.0, 3.0 );
        alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
        beta = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
        y = stdlib_base_dists_gamma_pdf( x, alpha, beta );
        printf( "x: %lf, α: %lf, β: %lf, f(x;α,β): %lf\n", x, alpha, beta, y );
    }
}

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

Copyright

Copyright © 2016-2026. The Stdlib Authors.