distr6 (version 1.3.6)

Gamma: Gamma Distribution Class

Description

Mathematical and statistical functions for the Gamma distribution, which is commonly used as the prior in Bayesian modelling, the convolution of exponential distributions, and to model waiting times.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Gamma$new(shape = 1, rate = 1, scale = NULL, mean = NULL, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
shape	numeric	shape parameter.
rate	numeric	inverse scale parameter.
scale	numeric	scale parameter.
mean	numeric	alternate scale parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Gamma distribution is parameterised with shape and either rate, scale or mean, all as positive numerics. These are related via, $$scale = 1/rate$$ $$mean = shape/rate$$ If mean is given then rate and scale are ignored. If scale is given then rate is ignored.

Public Variables

Variable	Return
name	Name of distribution.
short_name	Id of distribution.
description	Brief description of distribution.

Public Methods

Accessor Methods	Link
decorators	decorators
traits	traits
valueSupport	valueSupport
variateForm	variateForm
type	type
properties	properties
support	support
symmetry	symmetry
sup	sup
inf	inf
dmax	dmax
dmin	dmin
skewnessType	skewnessType
kurtosisType	kurtosisType

Statistical Methods Link pdf(x1, ..., log = FALSE, simplify = TRUE) pdf cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) cdf quantile(p, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) quantile.Distribution rand(n, simplify = TRUE) rand mean() mean.Distribution variance() variance stdev() stdev prec() prec cor() cor skewness() skewness kurtosis(excess = TRUE) kurtosis entropy(base = 2) entropy mgf(t) mgf cf(t) cf pgf(z) pgf median() median.Distribution iqr() iqr mode(which = "all") mode

Parameter Methods Link parameters(id) parameters getParameterValue(id, error = "warn") getParameterValue setParameterValue(..., lst = NULL, error = "warn") setParameterValue

Validation Methods Link liesInSupport(x, all = TRUE, bound = FALSE) liesInSupport liesInType(x, all = TRUE, bound = FALSE) liesInType

Representation Methods Link strprint(n = 2) strprint print(n = 2) print summary(full = T) summary.Distribution

Details

The Gamma distribution parameterised with shape, \(\alpha\), and rate, \(\beta\), is defined by the pdf, $$f(x) = (\beta^\alpha)/\Gamma(\alpha)x^{\alpha-1}exp(-x\beta)$$ for \(\alpha, \beta > 0\).

The distribution is supported on the Positive Reals.

References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.

See Also

listDistributions for all available distributions.

Examples

# NOT RUN {
Gamma$new(shape = 1, rate = 2)
Gamma$new(shape = 1, scale = 4)
Gamma$new(shape = 1, mean = 0.5)

# Default is shape = 1, rate = 1
x = Gamma$new(verbose = TRUE)

# Update parameters
# When any parameter is updated, all others are too!
x$setParameterValue(scale = 2)
x$parameters()

# d/p/q/r
x$pdf(5)
x$cdf(5)
x$quantile(0.42)
x$rand(4)

# Statistics
x$mean()
x$variance()

summary(x)

# }