Gammad-class {distr} | R Documentation |
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 can be created by calls of the form Gammad(scale, shape)
.
This object is a gamma distribution.
img
:"Reals"
: The space of the image of this distribution has got dimension 1
and the name "Real Space". param
:"GammaParameter"
: the parameter of this distribution (scale and shape),
declared at its instantiation r
:"function"
: generates random numbers (calls function rgamma)d
:"function"
: density function (calls function dgamma)p
:"function"
: cumulative function (calls function pgamma)q
:"function"
: inverse of the cumulative function (calls function qgamma)
Class "ExpOrGammaOrChisq"
, directly.
Class "AbscontDistribution"
, by class "ExpOrGammaOrChisq"
.
Class "UnivariateDistribution"
, by class "AbscontDistribution"
.
Class "Distribution"
, by class "UnivariateDistribution"
.
signature(.Object = "Gammad")
: initialize method signature(object = "Gammad")
: returns the slot scale
of the parameter of the distribution signature(object = "Gammad")
: modifies the slot scale
of the parameter of the distribution signature(object = "Gammad")
: returns the slot shape
of the parameter of the distribution 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.
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de
GammaParameter-class
AbscontDistribution-class
Reals-class
rgamma
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.