ppgnorm: A function to evaluate the p-generalized normal cdf

In pgnorm: The p-Generalized Normal Distribution

Description

The function evaluates the cdf of the univariate p-generalized normal distribution according to the density

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) .

Usage

ppgnorm(y, p, mean, sigma)

Arguments

y	A real number, the argument of the function.
p	A positive number expressing the form parameter of the distribution. The default is 2.
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 σ_p.

Value

A real number.

Author(s)

Steve Kalke

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<-ppgnorm(2,p=3) 

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