rpgnorm: A random number generator for the $p$-generalized normal distribution

Description

The function simulates the univariate $p$-generalized normal distribution by using one of the following methods: the $p$-generalized polar method (pgenpolar), the $p$-generalized rejecting polar method (pgenpolarrej), the Monty Python method (montypython), the Ziggurat method (ziggurat) and the method of Nardon and Pianca (nardonpianca).

Usage

rpgnorm(n, p, mean, sigma, method)

Arguments

The natural number of random variables to be simulated.

A positive number expressing the form parameter of the distribution. The default is 2. In case of the Monty Python method and the Ziggurat method, p can be chosen from $(1, \infty) \cup \{ 0.25, 0.45, 0.5, 0.6, 0.75 \} $.

mean

A real number expressing the expectation of the distribution. The default is 0.

sigma

A positive number expressing the standard deviation of the distribution. The default is $\sigma_p=p^{1/p} \, \sqrt{\Gamma(3/p)/ \Gamma(1/p)}$, the natural standard deviation of the $p$-generalized normal distribution.

method

A string expressing the method to be used for the simulation ("pgenpolar", "pgenpolarrej", "montypython", "ziggurat" or "nardonpianca"). The default is "nardonpianca".

Value

$n$-dimensional, real vector.

References

S. Kalke and W.-D. Richter (2013)."Simulation of the p-generalized Gaussian distribution." Journal of Statistical Computation and Simulation. Volume 83. Issue 4.