Class "Gammad"
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.
imgObject of class "Reals": The space of the image of this distribution has got dimension 1
and the name "Real Space".
paramObject of class "GammaParameter": the parameter of this distribution (scale and shape), declared at its instantiation
rObject of class "function": generates random numbers (calls function rgamma)
dObject of class "function": density function (calls function dgamma)
pObject of class "function": cumulative function (calls function pgamma)
qObject of class "function": inverse of the cumulative function (calls function qgamma)
.withArithlogical: used internally to issue warnings as to interpretation of arithmetics
.withSimlogical: used internally to issue warnings as to accuracy
.logExactlogical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExactlogical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetryobject 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
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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