Logarithm of Probability Density Function

Gamma distribution logarithm of 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-logpdf

Usage

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

logpdf( x, alpha, beta )

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

var y = logpdf( 2.0, 0.5, 1.0 );
// returns ~-2.919

y = logpdf( 0.1, 1.0, 1.0 );
// returns ~-0.1

y = logpdf( -1.0, 4.0, 2.0 );
// returns -Infinity

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

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

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

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

If provided alpha < 0, the function returns NaN.

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

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

var y = logpdf( 2.0, 0.0, 2.0 );
// returns -Infinity

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

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

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

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

logpdf.factory( alpha, beta )

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

var mylogpdf = logpdf.factory( 3.0, 1.5 );

var y = mylogpdf( 1.0 );
// returns ~-0.977

y = mylogpdf( 4.0 );
// returns ~-2.704

Examples

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

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 = logpdf( x, alpha, beta );
    console.log( 'x: %d, α: %d, β: %d, ln(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.