distr (version 2.9.5)

Gammad-class: Class "Gammad"

Description

The Gammad distribution with parameters shape \(=\alpha\), by default = 1, and scale \(=\sigma\), by default = 1, has density $$ d(x)= \frac{1}{{\sigma}^{\alpha}\Gamma(\alpha)} {x}^{\alpha-1} e^{-x/\sigma}% $$ for \(x > 0\), \(\alpha > 0\) and \(\sigma > 0\). The mean and variance are \(E(X) = \alpha\sigma\) and \(Var(X) = \alpha\sigma^2\). C.f. rgamma

Objects from the Class

Objects can be created by calls of the form Gammad(scale, shape). This object is a gamma distribution.

Slots

img

Object of class "Reals": The space of the image of this distribution has got dimension 1 and the name "Real Space".

param

Object of class "GammaParameter": the parameter of this distribution (scale and shape), declared at its instantiation

r

Object of class "function": generates random numbers (calls function rgamma)

d

Object of class "function": density function (calls function dgamma)

p

Object of class "function": cumulative function (calls function pgamma)

q

Object of class "function": inverse of the cumulative function (calls function qgamma)

.withArith

logical: used internally to issue warnings as to interpretation of arithmetics

.withSim

logical: used internally to issue warnings as to accuracy

.logExact

logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function

.lowerExact

logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

Symmetry

object of class "DistributionSymmetry"; used internally to avoid unnecessary calculations.

Extends

Class "ExpOrGammaOrChisq", directly.
Class "AbscontDistribution", by class "ExpOrGammaOrChisq".
Class "UnivariateDistribution", by class "AbscontDistribution".
Class "Distribution", by class "UnivariateDistribution".

Methods

initialize

signature(.Object = "Gammad"): initialize method

scale

signature(object = "Gammad"): returns the slot scale of the parameter of the distribution

scale<-

signature(object = "Gammad"): modifies the slot scale of the parameter of the distribution

shape

signature(object = "Gammad"): returns the slot shape of the parameter of the distribution

shape<-

signature(object = "Gammad"): modifies the slot shape of the parameter of the distribution

+

signature(e1 = "Gammad", e2 = "Gammad"): For the Gamma distribution we use its closedness under convolutions.

*

signature(e1 = "Gammad", e2 = "numeric"): For the Gamma distribution we use its closedness under positive scaling transformations.

Author

Thomas Stabla ,
Florian Camphausen ,
Peter Ruckdeschel ,
Matthias Kohl

See Also

GammaParameter-class AbscontDistribution-class Reals-class rgamma

Examples

G <- Gammad(scale=1,shape=1) # G is a gamma distribution with scale=1 and shape=1.
r(G)(1) # one random number generated from this distribution, e.g. 0.1304441
d(G)(1) # Density of this distribution is 0.3678794 for x=1.
p(G)(1) # Probability that x<1 is 0.6321206.
q(G)(.1) # Probability that x<0.1053605 is 0.1.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
scale(G) # scale of this distribution is 1.
scale(G) <- 2 # scale of this distribution is now 2.