UNU.RAN random variate generator for the Gamma distribution
with parameters shape and scale.
It also allows sampling from the truncated distribution.
[Special Generator] -- Sampling Function: Gamma.
urgamma(n, shape, scale=1, lb=0, ub=Inf)
size of required sample.
(strictly positive) shape parameter.
(strictly positive) scale parameter.
lower bound of (truncated) distribution
upper bound of (truncated) distribution
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
If scale is omitted, it assumes the default value of 1.
The Gamma distribution with parameters shape \(=\alpha\)
and scale \(=\sigma\) has density
$$
f(x)= \frac{1}{{\sigma}^{\alpha}\Gamma(\alpha)} {x}^{\alpha-1} e^{-x/\sigma}
$$
for \(x \ge 0\), \(\alpha > 0\) and \(\sigma > 0\).
(Here \(\Gamma(\alpha)\) is the function implemented by R's
gamma() and defined in its help.)
The generation algorithm uses fast numerical inversion. The parameters
lb and ub can be used to generate variates from
the Gamma distribution truncated to the interval (lb,ub).
W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg
runif and .Random.seed about random number
generation, unuran for the UNU.RAN class, and
rgamma for the R built-in generator.
## Create a sample of size 1000
x <- urgamma(n=1000,shape=2)
Run the code above in your browser using DataLab