urgamma function

UNU.RAN Gamma random variate generator

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)

Arguments

• n: size of required sample.
• shape: (strictly positive) shape parameter.
• scale: (strictly positive) scale parameter.
• lb: lower bound of (truncated) distribution
• ub: upper bound of (truncated) distribution

Details

If scale is omitted, it assumes the default value of 1.

The Gamma distribution with parameters shape $= a$

and scale $= s$ has density

for $x \ge 0$, $a > 0$ and $s > 0$. (Here $Gamma(a)$ is the function implemented by '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).

See Also

runif and .Random.seed about random number generation, unuran for the UNU.RAN class, and rgamma for the built-in generator.

References

W. H"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg

Author(s)

Josef Leydold and Wolfgang H"ormann unuran@statmath.wu.ac.at .

Note

This function is a wrapper for the UNU.RAN class in . Compared to rgamma, urgamma is faster, especially for larger sample sizes. However, in opposition to rgamma vector arguments are ignored, i.e. only the first entry is used.

Examples

## Create a sample of size 1000
x <- urgamma(n=1000,shape=2)