dpgnorm {pgnorm}

A function to evaluate the p-generalized normal density

Description

The function evaluates the density f(x,p,mean,sigma) of the univariate p-generalized normal distribution according to

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).

Usage

dpgnorm(y, p, mean, sigma)

Arguments

y

The real 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 \sigma_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<-dpgnorm(0,3,1,2)