pgnorm-package: The p-Generalized Normal Distribution

In pgnorm: 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 σ. The pdf of this distribution is given by

f(x,p,mean,σ)=(σ_p/ σ) \, C_p \, \exp ≤ft( - ≤ft( \frac{σ_p}{σ } \right)^p \frac{≤ft| x-mean \right|^p}{p} \right) ,

where C_p=p^{1-1/p}/2/Γ(1/p) and σ_p^2=p^{2/p} \, Γ(3/p)/Γ(1/p), which becomes

f(x,p,mean,σ)=C_p \, \exp ≤ft( - \frac{≤ft| x \right|^p}{p} \right),

if σ=σ_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.

Details

Package:	pgnorm
Type:	Package
Version:	2.0
Date:	2015-11-23
License:	GPL (>= 2)
LazyLoad:	yes

Author(s)

Steve Kalke <[e-mail]>

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.

Examples

y<-rpgnorm(10,3)

pgnorm documentation built on May 1, 2019, 7:55 p.m.