pnormp: Probability function of an exponential power distribution

Description

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

Usage

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

Value

pnormp gives the probability of an exponential power distribution.

Arguments

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 $P [X\leq x]$, otherwise, $P[X>x]$.
log.pr: Logical; if TRUE, probabilities $pr$ are given as $log(pr)$.

Author

Angelo M. Mineo

Details

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

$$f(x) = \frac{1}{2 p^{(1/p)} \Gamma(1+1/p) \sigma_p} e^{-\frac{|x - \mu|^p}{p \sigma_p^p}}$$

where $\mu$ is the location parameter, $\sigma_p$ 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 $p\rightarrow\infty$ the exponential power distribution becomes the Uniform Distribution.

Examples

Run this code

## 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)")

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