Runuran (version 0.40)

udpowerexp: UNU.RAN object for Powerexponential distribution

Description

Create UNU.RAN object for a Powerexponential (Subbotin) distribution with shape parameter shape.

[Distribution] -- Powerexponential (Subbotin).

Usage

udpowerexp(shape, lb=-Inf, ub=Inf)

Value

An object of class "unuran.cont".

Arguments

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 domain of the distribution can be truncated to the interval (lb,ub).

References

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

unuran.cont.

Examples

## Create distribution object for powerexponential distribution
distr <- udpowerexp(shape=4)
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)