qaep {AEP} R Documentation

## Computing the quantile function of asymmetric exponential power (AEP) distribution.

### Description

Computes the quantile function of AEP distribution given by

 F_{X}^{-1}(u|\Theta)= \mu-\sigma(1-\epsilon)\biggl[\frac{\gamma\bigl(\frac{1-\epsilon-2u}{1-\epsilon},\frac{1}{\alpha}\bigr)}{\Gamma\bigl(\frac{1}{\alpha}\bigr)}\biggr]^{\frac{1}{\alpha}},~{{}}~u\leq \frac{1-\epsilon}{2}, 

 F_{X}^{-1}(u|\Theta)= \mu+\sigma(1+\epsilon)\biggl[\frac{\gamma\bigl(\frac{2u+\epsilon-1}{1+\epsilon},\frac{1}{\alpha}\bigr)}{\Gamma\bigl(\frac{1}{\alpha}\bigr)}\biggr]^{\frac{1}{\alpha}},~{{}}~u> \frac{1-\epsilon}{2}.\\ 

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

\gamma(u,\nu) =\int_{0}^{u}t^{\nu-1}\exp\bigl\{-t\bigr\}dt, ~\nu>0.

### Usage

qaep(u, alpha, sigma, mu, epsilon)

### Arguments

 u Numeric vector with values in (0,1) whose quantiles are desired. alpha Tail thickness parameter. sigma Scale parameter. mu Location parameter. epsilon Skewness parameter.

### Value

A vector of length n, consists of the random generated values from AEP distribution.

Mahdi Teimouri

### Examples

qaep(runif(1), alpha = 1.5, sigma = 1, mu = 0, epsilon = 0.5)


[Package AEP version 0.1.4 Index]