pnormp: Probability function of an exponential power distribution
In normalp: Routines for Exponential Power Distribution

Description Usage Arguments Details Value Author(s) See Also Examples

Probability function for the exponential power distribution with location parameter mu, scale parameter sigmap and shape parameter p.

1	pnormp(q, mu=0, sigmap=1, p=2, lower.tail=TRUE, log.pr=FALSE)

`q`	Vector of quantiles.
`mu`	Vector of location parameters.
`sigmap`	Vector of scale parameters.
`p`	Shape parameter.
`lower.tail`	Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X>x].
`log.pr`	Logical; if TRUE, probabilities pr are given as log(pr).

If mu, sigmap or p are not specified they assume the default values 0, 1 and 2, respectively. The exponential power distribution has density function

f(x) = 1/(2 p^(1/p) Gamma(1+1/p) sigmap) exp{-|x - mu|^p/(p sigmap^p)}

where mu is the location parameter, sigmap the scale parameter and p the shape parameter. When p=2 the exponential power distribution becomes the Normal Distribution, when p=1 the exponential power distribution becomes the Laplace Distribution, when p->infinity the exponential power distribution becomes the Uniform Distribution.

pnormp gives the probability of an exponential power distribution.

Angelo M. Mineo

Normal for the Normal distribution, Uniform for the Uniform distribution, and Special for the Gamma function.

## Compute the distribution function for a vector x with mu=0, sigmap=1 and p=1.5
## At the end we have the graph of the exponential power distribution function with p=1.5.
x <- c(-1, 1)
pr <- pnormp(x, p=1.5)
print(pr)
plot(function(x) pnormp(x, p=1.5), -4, 4,
          main = "Exponential Power Distribution Function (p=1.5)", ylab="F(x)")