Gammad-class | R Documentation |
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 can be created by calls of the form Gammad(scale, shape)
.
This object is a gamma distribution.
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.
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@uni-oldenburg.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.
## 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.
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