paep: Computing the cumulative distribution function (cdf) of...

In AEP: Statistical Modelling for Asymmetric Exponential Power Distribution

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

Description

Computes the cdf of AEP distribution given by

F_{X}(x|Θ)= \frac{1-ε}{2}-\frac{1-ε}{2 Γ\bigl(1+\frac{1}{α}\bigr)} γ\Bigl(\Big|\frac{μ-x}{σ(1-ε)}\Big|^{α},\frac{1}{α}\Bigr),~{}~x < μ,

F_{X}(x|Θ)= \frac{1-ε}{2}+\frac{1+ε}{2 Γ\bigl(1+\frac{1}{α}\bigr)} γ\Bigl(\Big|\frac{x-μ}{σ(1+ε)}\Big|^{α},\frac{1}{α}\Bigr),~{{}}~x ≥q μ,

where -∞<x<+∞, Θ=(α,σ,μ,ε)^T with 0<α ≤q 2, σ> 0, -∞<μ<∞, and -1<ε<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|Θ)\bigr) is returned.
lower.tail	If FALSE, then 1-F_{X}(x|Θ) 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)

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