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Erlang

Erlang distribution constructor.

Installation

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

Alternatively,

To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
If you are using Deno, visit the deno branch (see README for usage intructions).
For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the 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.

Usage

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

Erlang( [k, lambda] )

Returns an Erlang distribution object.

var erlang = new Erlang();

var mode = erlang.mode;
// returns 0.0

By default, k = 1.0 and lambda = 1.0. To create a distribution having a different k (shape parameter) and lambda (rate parameter), provide the corresponding arguments.

var erlang = new Erlang( 2, 4.0 );

var mode = erlang.mode;
// returns 0.25

erlang

An Erlang distribution object has the following properties and methods...

Writable Properties

erlang.k

Shape parameter of the distribution. k must be a positive integer.

var erlang = new Erlang();

var k = erlang.k;
// returns 1.0

erlang.k = 3.0;

k = erlang.k;
// returns 3.0

erlang.lambda

Rate parameter of the distribution. lambda must be a positive number.

var erlang = new Erlang( 2, 4.0 );

var lambda = erlang.lambda;
// returns 4.0

erlang.lambda = 3.0;

lambda = erlang.lambda;
// returns 3.0

Computed Properties

Erlang.prototype.entropy

Returns the differential entropy.

var erlang = new Erlang( 4, 12.0 );

var entropy = erlang.entropy;
// returns ~-0.462

Erlang.prototype.kurtosis

Returns the excess kurtosis.

var erlang = new Erlang( 4, 12.0 );

var kurtosis = erlang.kurtosis;
// returns 1.5

Erlang.prototype.mean

Returns the expected value.

var erlang = new Erlang( 4, 12.0 );

var mu = erlang.mean;
// returns ~0.333

Erlang.prototype.mode

Returns the mode.

var erlang = new Erlang( 4, 12.0 );

var mode = erlang.mode;
// returns 0.25

Erlang.prototype.skewness

Returns the skewness.

var erlang = new Erlang( 4, 12.0 );

var skewness = erlang.skewness;
// returns 1.0

Erlang.prototype.stdev

Returns the standard deviation.

var erlang = new Erlang( 4, 12.0 );

var s = erlang.stdev;
// returns ~0.167

Erlang.prototype.variance

Returns the variance.

var erlang = new Erlang( 4, 12.0 );

var s2 = erlang.variance;
// returns ~0.028

Methods

Erlang.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var erlang = new Erlang( 2, 4.0 );

var y = erlang.cdf( 0.5 );
// returns ~0.594

Erlang.prototype.logpdf( x )

Evaluates the natural logarithm of the probability density function (PDF).

var erlang = new Erlang( 2, 4.0 );

var y = erlang.logpdf( 0.8 );
// returns ~-0.65

Erlang.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var erlang = new Erlang( 2, 4.0 );

var y = erlang.mgf( 0.5 );
// returns ~1.306

Erlang.prototype.pdf( x )

Evaluates the probability density function (PDF).

var erlang = new Erlang( 2, 4.0 );

var y = erlang.pdf( 0.8 );
// returns ~0.522

Erlang.prototype.quantile( p )

Evaluates the quantile function at probability p.

var erlang = new Erlang( 2, 4.0 );

var y = erlang.quantile( 0.5 );
// returns ~0.42

y = erlang.quantile( 1.9 );
// returns NaN

Examples

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

var erlang = new Erlang( 2, 4.0 );

var mu = erlang.mean;
// returns 0.5

var mode = erlang.mode;
// returns 0.25

var s2 = erlang.variance;
// returns 0.125

var y = erlang.cdf( 0.8 );
// returns ~0.829

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.

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