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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.