paep {AEP}

Computing the cumulative distribution function (cdf) of asymmetric exponential power (AEP) distribution.

Description

Computes the cdf of AEP distribution given by

F_{X}(x|\Theta)= \frac{1-\epsilon}{2}-\frac{1-\epsilon}{2 \Gamma\bigl(1+\frac{1}{\alpha}\bigr)} \gamma\Bigl(\Big|\frac{\mu-x}{\sigma(1-\epsilon)}\Big|^{\alpha},\frac{1}{\alpha}\Bigr),~{}~x < \mu,

F_{X}(x|\Theta)= \frac{1-\epsilon}{2}+\frac{1+\epsilon}{2 \Gamma\bigl(1+\frac{1}{\alpha}\bigr)} \gamma\Bigl(\Big|\frac{x-\mu}{\sigma(1+\epsilon)}\Big|^{\alpha},\frac{1}{\alpha}\Bigr),~{{}}~x \geq \mu,

where -\infty<x<+\infty, \Theta=(\alpha,\sigma,\mu,\epsilon)^T with 0<\alpha \leq 2, \sigma> 0, -\infty<\mu<\infty, and -1<\epsilon<1.

Usage

paep(x, alpha, sigma, mu, epsilon, log.p = FALSE, lower.tail = TRUE)

Arguments

x

Vector of observations.

alpha

Tail thickness parameter.

sigma

Scale parameter.

mu

Location parameter.

epsilon

Skewness parameter.

log.p

If TRUE, then log \bigl(F_{X}(x|\Theta)\bigr) is returned.

lower.tail

If FALSE, then 1-F_{X}(x|\Theta) is returned.

Value

Computed cdf of AEP distribution at points of vector x.

Author(s)

Mahdi Teimouri

Examples

paep(x = 2, alpha = 1.5, sigma = 1, mu = 0, epsilon = 0.5, log.p = FALSE, lower.tail = TRUE)