Gamma

Gamma distribution constructor.

Installation

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

Usage

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

Gamma( [alpha, beta] )

Returns a gamma distribution object.

var gamma = new Gamma();

var mode = gamma.mode;
// returns 0.0

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

var gamma = new Gamma( 2.0, 4.0 );

var mu = gamma.mean;
// returns 0.5

gamma

A gamma distribution object has the following properties and methods...

Writable Properties

gamma.alpha

Shape parameter of the distribution. alpha must be a positive number.

var gamma = new Gamma();

var alpha = gamma.alpha;
// returns 1.0

gamma.alpha = 3.0;

alpha = gamma.alpha;
// returns 3.0

gamma.beta

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

var gamma = new Gamma( 2.0, 4.0 );

var b = gamma.beta;
// returns 4.0

gamma.beta = 3.0;

b = gamma.beta;
// returns 3.0

Computed Properties

Gamma.prototype.entropy

Returns the differential entropy.

var gamma = new Gamma( 4.0, 12.0 );

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

Gamma.prototype.kurtosis

Returns the excess kurtosis.

var gamma = new Gamma( 4.0, 12.0 );

var kurtosis = gamma.kurtosis;
// returns 1.5

Gamma.prototype.mean

Returns the expected value.

var gamma = new Gamma( 4.0, 12.0 );

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

Gamma.prototype.mode

Returns the mode.

var gamma = new Gamma( 4.0, 12.0 );

var mode = gamma.mode;
// returns 0.25

Gamma.prototype.skewness

Returns the skewness.

var gamma = new Gamma( 4.0, 12.0 );

var skewness = gamma.skewness;
// returns 1.0

Gamma.prototype.stdev

Returns the standard deviation.

var gamma = new Gamma( 4.0, 12.0 );

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

Gamma.prototype.variance

Returns the variance.

var gamma = new Gamma( 4.0, 12.0 );

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

Methods

Gamma.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var gamma = new Gamma( 2.0, 4.0 );

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

Gamma.prototype.logcdf( x )

Evaluates the natural logarithm of the cumulative distribution function (CDF).

var gamma = new Gamma( 2.0, 4.0 );

var y = gamma.logcdf( 0.5 );
// returns ~-0.521

Gamma.prototype.logpdf( x )

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

var gamma = new Gamma( 2.0, 4.0 );

var y = gamma.logpdf( 0.8 );
// returns ~-0.651

Gamma.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var gamma = new Gamma( 2.0, 4.0 );

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

Gamma.prototype.pdf( x )

Evaluates the probability density function (PDF).

var gamma = new Gamma( 2.0, 4.0 );

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

Gamma.prototype.quantile( p )

Evaluates the quantile function at probability p.

var gamma = new Gamma( 2.0, 4.0 );

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

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

Examples

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

var gamma = new Gamma( 2.0, 4.0 );

var mu = gamma.mean;
// returns 0.5

var mode = gamma.mode;
// returns 0.25

var s2 = gamma.variance;
// returns 0.125

var y = gamma.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.

Copyright

Copyright © 2016-2024. The Stdlib Authors.