@stdlib/stats-base-dists-gamma-pdf
v0.3.1TypeScript
Gamma distribution probability density function (PDF).
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Published by The Stdlib Authors
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About stdlib...
Probability Density Function
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> [Gamma][gamma-distribution] distribution probability density function (PDF).
The [probability density function][pdf] (PDF) for a [gamma][gamma-distribution] random variable is
where α > 0 is the shape parameter and β > 0 is the rate parameter.
Installation
``bash`
npm install @stdlib/stats-base-dists-gamma-pdf
Usage
`javascript`
var pdf = require( '@stdlib/stats-base-dists-gamma-pdf' );
#### pdf( x, alpha, beta )
Evaluates the [probability density function][pdf] (PDF) for a [gamma][gamma-distribution] distribution with parameters alpha (shape parameter) and beta (rate parameter).
`javascript
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.
`javascript
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.
`javascript`
var y = pdf( 2.0, -0.5, 1.0 );
// returns NaN
If provided alpha = 0, the function evaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at 0.
`javascript
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.
`javascript
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][pdf] of a [gamma][gamma-distribution] distribution with parameters alpha (shape parameter) and beta (rate parameter).
`javascript
var mypdf = pdf.factory( 3.0, 1.5 );
var y = mypdf( 1.0 );
// returns ~0.377
y = mypdf( 4.0 );
// returns ~0.067
`
Examples
`javascript
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
$3
`c`
#include "stdlib/stats/base/dists/gamma/pdf.h"
#### stdlib_base_dists_gamma_pdf( x, alpha, beta )
Evaluates the [probability density function][pdf] (PDF) for a [gamma][gamma-distribution] distribution with parameters alpha (shape parameter) and beta (rate parameter).
`c`
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.[in] double
- alpha: shape parameter.[in] double
- beta: rate parameter.
`c`
double stdlib_base_dists_gamma_pdf( const double x, const double alpha, const double beta );
$3
`c
#include "stdlib/stats/base/dists/gamma/pdf.h"
#include "stdlib/constants/float64/eps.h"
#include
#include
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][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-gamma-pdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-pdf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-gamma-pdf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-pdf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-gamma-pdf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-pdf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-gamma-pdf/blob/main/branches.md
[gamma-distribution]: https://en.wikipedia.org/wiki/Gamma_distribution
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function
[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution