Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function (PDF) for an Erlang distribution.

The probability density function (PDF) for an Erlang random variable is

where k is the shape parameter and lambda is the rate parameter.

Installation

npm install @stdlib/stats-base-dists-erlang-logpdf

Usage

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

logpdf( x, k, lambda )

Evaluates the natural logarithm of the probability density function (PDF) for an Erlang distribution with parameters k (shape parameter) and lambda (rate parameter).

var y = logpdf( 0.1, 1, 1.0 );
// returns ~-0.1

y = logpdf( 0.5, 2, 2.5 );
// returns ~-0.111

y = logpdf( -1.0, 4, 2.0 );
// returns -Infinity

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

var y = logpdf( NaN, 1, 1.0 );
// returns NaN

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

y = logpdf( 0.0, 1, NaN );
// returns NaN

If not provided a nonnegative integer for k, the function returns NaN.

var y = logpdf( 2.0, -2, 0.5 );
// returns NaN

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

If provided k = 0, the function evaluates the logarithm of the PDF of 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 lambda <= 0, the function returns NaN.

var y = logpdf( 2.0, 1, 0.0 );
// returns NaN

y = logpdf( 2.0, 1, -1.0 );
// returns NaN

logpdf.factory( k, lambda )

Returns a function for evaluating the PDF for an Erlang distribution with parameters k (shape parameter) and lambda (rate parameter).

var mylogpdf = logpdf.factory( 3, 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 round = require( '@stdlib/math-base-special-round' );
var logpdf = require( '@stdlib/stats-base-dists-erlang-logpdf' );

var lambda;
var k;
var x;
var y;
var i;

for ( i = 0; i < 20; i++ ) {
    x = randu() * 10.0;
    k = round( randu() * 10.0 );
    lambda = randu() * 5.0;
    y = logpdf( x, k, lambda );
    console.log( 'x: %d, k: %d, λ: %d, ln(f(x;k,λ)): %d', x.toFixed( 4 ), k, lambda.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.