pgnorm-package: The $p$-Generalized Normal Distribution
Description
The pgnorm-package includes routines to evaluate (cdf,pdf) and simulate the univariate $p$-generalized normal distribution with form parameter $p$, expectation $mean$ and standard deviation $\sigma$. The pdf of this distribution is given by $$f(x,p,mean,\sigma)=(\sigma_p/ \sigma) \, C_p \, \exp \left( - \left( \frac{\sigma_p}{\sigma } \right)^p \frac{\left| x-mean \right|^p}{p} \right) ,$$ where $C_p=p^{1-1/p}/2/\Gamma(1/p)$ and $\sigma_p^2=p^{2/p} \, \Gamma(3/p)/\Gamma(1/p)$, which becomes $$f(x,p,mean,\sigma)=C_p \, \exp \left( - \frac{\left| x \right|^p}{p} \right),$$ if $\sigma=\sigma_p$ and $mean=0$. The random number generation can be realized with one of five different simulation methods including the $p$-generalized polar method, the $p$-generalized rejecting polar method, the Monty Python method, the Ziggurat method and the method of Nardon and Pianca. Additionally to the simulation of the p-generalized normal distribution, the related $p$-generalized uniform distribution on the $p$-generalized unit circle and the corresponding angular distribution can be simulated by using the functions "rpgunif" and "rpgangular", respectively.
S. Kalke and W.-D. Richter (2013)."Simulation of the p-generalized Gaussian distribution." Journal of Statistical Computation and Simulation. Volume 83. Issue 4.