Erlang distribution probability density function (PDF).
APACHE-2.0 License
Erlang distribution probability density function (PDF).
The probability density function (PDF) for an Erlang random variable is
f(x; k,\lambda)={\lambda^k x^{k-1} e^{-\lambda x} \over (k-1)!} 1(x \ge 0)
where k
is the shape parameter and lambda
is the rate parameter.
npm install @stdlib/stats-base-dists-erlang-pdf
Alternatively,
script
tag without installation and bundlers, use the ES Module available on the esm
branch (see README).deno
branch (see README for usage intructions).umd
branch (see README).The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
var pdf = require( '@stdlib/stats-base-dists-erlang-pdf' );
Evaluates the probability density function (PDF) for an Erlang distribution with parameters k
(shape parameter) and lambda
(rate parameter).
var y = pdf( 0.1, 1, 1.0 );
// returns ~0.905
y = pdf( 0.5, 2, 2.5 );
// returns ~0.895
y = pdf( -1.0, 4, 2.0 );
// returns 0.0
If provided NaN
as any argument, the function returns NaN
.
var y = pdf( NaN, 1, 1.0 );
// returns NaN
y = pdf( 0.0, NaN, 1.0 );
// returns NaN
y = pdf( 0.0, 1, NaN );
// returns NaN
If not provided a nonnegative integer for k
, the function returns NaN
.
var y = pdf( 2.0, -2, 0.5 );
// returns NaN
y = pdf( 2.0, 0.5, 0.5 );
// returns NaN
If provided k = 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 lambda <= 0
, the function returns NaN
.
var y = pdf( 2.0, 1, 0.0 );
// returns NaN
y = pdf( 2.0, 1, -1.0 );
// returns NaN
Returns a function
for evaluating the PDF for an Erlang distribution with parameters k
(shape parameter) and lambda
(rate parameter).
var mypdf = pdf.factory( 3, 1.5 );
var y = mypdf( 1.0 );
// returns ~0.377
y = mypdf( 4.0 );
// returns ~0.067
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var pdf = require( '@stdlib/stats-base-dists-erlang-pdf' );
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 = pdf( x, k, lambda );
console.log( 'x: %d, k: %d, λ: %d, f(x;k,λ): %d', x.toFixed( 4 ), k, lambda.toFixed( 4 ), y.toFixed( 4 ) );
}
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.
See LICENSE.
Copyright © 2016-2024. The Stdlib Authors.