Description Objects from the Class Slots Extends Methods Author(s) See Also Examples

### Description

The Gammad distribution with parameters `shape` = a, by default `= 1`, and `scale` = s, by default `= 1`, has density

d(x)= 1/(s^a Gamma(a)) x^(a-1) e^-(x/s)

for x > 0, a > 0 and s > 0. The mean and variance are E(X) = a*s and Var(X) = a*s^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(s)

Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de

`GammaParameter-class` `AbscontDistribution-class` `Reals-class` `rgamma`

### Examples

 ```1 2 3 4 5 6 7``` ```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. scale(G) # scale of this distribution is 1. scale(G) <- 2 # scale of this distribution is now 2. ```

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