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.

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 $$\alpha, \beta > 0$$.

Distribution support

The distribution is supported on the Positive Reals.

Default Parameterisation

Gamma(shape = 1, rate = 1)

N/A

N/A

References

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

Other continuous distributions: Arcsine, BetaNoncentral, Beta, Cauchy, ChiSquaredNoncentral, ChiSquared, Dirichlet, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gompertz, Gumbel, InverseGamma, Laplace, Logistic, Loglogistic, Lognormal, MultivariateNormal, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull

Other univariate distributions: Arcsine, Arrdist, Bernoulli, BetaNoncentral, Beta, Binomial, Categorical, Cauchy, ChiSquaredNoncentral, ChiSquared, Degenerate, DiscreteUniform, Empirical, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Geometric, Gompertz, Gumbel, Hypergeometric, InverseGamma, Laplace, Logarithmic, Logistic, Loglogistic, Lognormal, Matdist, NegativeBinomial, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull, WeightedDiscrete

Super classes

distr6::Distribution -> distr6::SDistribution -> Gamma

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

alias

Alias of the distribution.

packages

Packages required to be installed in order to construct the distribution.

Methods

Inherited methods

Method new()

Creates a new instance of this R6 class.

Arguments

...

Unused.

Method mode()

The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).

Arguments

...

Unused.

Method skewness()

The skewness of a distribution is defined by the third standardised moment, $$sk_X = E_X[\frac{x - \mu}{\sigma}^3]$$ where $$E_X$$ is the expectation of distribution X, $$\mu$$ is the mean of the distribution and $$\sigma$$ is the standard deviation of the distribution.

Arguments

excess

(logical(1))
If TRUE (default) excess kurtosis returned.

...

Unused.

Method entropy()

The entropy of a (discrete) distribution is defined by $$- \sum (f_X)log(f_X)$$ where $$f_X$$ is the pdf of distribution X, with an integration analogue for continuous distributions.

Arguments

t

(integer(1))
t integer to evaluate function at.

...

Unused.

Method cf()

The characteristic function is defined by $$cf_X(t) = E_X[exp(xti)]$$ where X is the distribution and $$E_X$$ is the expectation of the distribution X.

Arguments

z

(integer(1))
z integer to evaluate probability generating function at.

...

Unused.

Method clone()

The objects of this class are cloneable with this method.

Usage

Gamma\$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.