paep {AEP} R Documentation

## 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.

Mahdi Teimouri

### Examples

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


[Package AEP version 0.1.4 Index]