qaep {AEP}

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.

Author(s)

Mahdi Teimouri

Examples

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