Runuran (version 0.40)

urpowerexp: UNU.RAN Powerexponential random variate generator

Description

UNU.RAN random variate generator for the Powerexponential (Subbotin) distribution with shape parameter shape. It also allows sampling from the truncated distribution.

[Special Generator] -- Sampling Function: Powerexponential (Subbotin).

Usage

urpowerexp(n, shape, lb = -Inf, ub = Inf)

Arguments

n

size of required sample.

shape

(strictly positive) shape parameter.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

Details

The Powerexponential distribution with parameter shape \(=\tau\) has density $$ f(x) = \frac{1}{2\Gamma(1+1/\tau)} \exp(-|x|^\tau) $$ for all \(x\) and \(\tau > 0\). (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 Powerexponential distribution truncated to the interval (lb,ub).

References

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

N.L. Johnson, S. Kotz, and N. Balakrishnan (1995): Continuous Univariate Distributions, Volume 2. 2nd edition, John Wiley & Sons, Inc., New York. Chap.24, p.195.

See Also

runif and .Random.seed about random number generation and unuran for the UNU.RAN class.

Examples

## Create a sample of size 1000
x <- urpowerexp(n=1000, shape=4)