Class "Gamma"

The Gamma 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 from the Class

Objects can be created by calls of the form Gamma(scale, shape). This object is a gamma distribution.


Class "AbscontDistribution", directly. Class "UnivariateDistribution", by class "AbscontDistribution". Class "Distribution", by class "AbscontDistribution".

See Also

GammaParameter-class AbscontDistribution-class Reals-class rgamma

  • Gamma-class
  • Gamma
  • initialize,Gamma-method
G=Gamma(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.
Documentation reproduced from package distr, version 1.4, License: GPL (version 2 or later)

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