@stdlib/stats-base-dists-erlang-cdf
v0.2.2
Published
Erlang distribution cumulative distribution function (CDF).
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Cumulative Distribution Function
Erlang distribution cumulative distribution function.
The cumulative distribution function for a Erlang random variable is
where k
is the shape parameter and lambda
is the rate parameter. The Erlang distribution is a special case of the gamma distribution, as k
is constrained to the natural numbers.
Installation
npm install @stdlib/stats-base-dists-erlang-cdf
Usage
var cdf = require( '@stdlib/stats-base-dists-erlang-cdf' );
cdf( x, k, lambda )
Evaluates the cumulative distribution function (CDF) for an Erlang distribution with parameters k
(shape parameter) and lambda
(rate parameter).
var y = cdf( 2.0, 1, 1.0 );
// returns ~0.865
y = cdf( 2.0, 3, 1.0 );
// returns ~0.323
y = cdf( -1.0, 2, 2.0 );
// returns 0.0
y = cdf( -Infinity, 4, 2.0 );
// returns 0.0
y = cdf( +Infinity, 4, 2.0 );
// returns 1.0
If provided NaN
as any argument, the function returns NaN
.
var y = cdf( NaN, 1, 1.0 );
// returns NaN
y = cdf( 0.0, NaN, 1.0 );
// returns NaN
y = cdf( 0.0, 1, NaN );
// returns NaN
If not provided a nonnegative integer for k
, the function returns NaN
.
var y = cdf( 2.0, -2, 0.5 );
// returns NaN
y = cdf( 2.0, 0.5, 0.5 );
// returns NaN
If provided k = 0
, the function evaluates the CDF of a degenerate distribution centered at 0
.
var y = cdf( 2.0, 0.0, 2.0 );
// returns 1.0
y = cdf( -2.0, 0.0, 2.0 );
// returns 0.0
y = cdf( 0.0, 0.0, 2.0 );
// returns 1.0
If provided lambda <= 0
, the function returns NaN
.
var y = cdf( 2.0, 1, 0.0 );
// returns NaN
y = cdf( 2.0, 1, -5.0 );
// returns NaN
cdf.factory( k, lambda )
Returns a function for evaluating the cumulative distribution function for an Erlang distribution with parameters k
(shape parameter) and lambda
(rate parameter).
var mycdf = cdf.factory( 2, 0.5 );
var y = mycdf( 6.0 );
// returns ~0.801
y = mycdf( 2.0 );
// returns ~0.264
Examples
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var cdf = require( '@stdlib/stats-base-dists-erlang-cdf' );
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 = cdf( 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 ) );
}
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.