Gammad-class {distr}R Documentation

Class "Gammad"

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)

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@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de

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.
scale(G) # scale of this distribution is 1.
scale(G) <- 2 # scale of this distribution is now 2.

[Package distr version 2.0.6 Index]