qaep: Computing the quantile function of asymmetric exponential...

In AEP: Statistical Modelling for Asymmetric Exponential Power Distribution

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

Description

Computes the quantile function of AEP distribution given by

F_{X}^{-1}(u|Θ)= μ-σ(1-ε)\biggl[\frac{γ\bigl(\frac{1-ε-2u}{1-ε},\frac{1}{α}\bigr)}{Γ\bigl(\frac{1}{α}\bigr)}\biggr]^{\frac{1}{α}},~{{}}~u≤q \frac{1-ε}{2},

F_{X}^{-1}(u|Θ)= μ+σ(1+ε)\biggl[\frac{γ\bigl(\frac{2u+ε-1}{1+ε},\frac{1}{α}\bigr)}{Γ\bigl(\frac{1}{α}\bigr)}\biggr]^{\frac{1}{α}},~{{}}~u> \frac{1-ε}{2}.\\

where -∞<x<+∞, Θ=(α,σ,μ,ε)^T with 0<α ≤q 2, σ> 0, -∞<μ<∞, -1<ε<1, and

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

AEP documentation built on Sept. 7, 2022, 5:06 p.m.