Computing the quantile function of asymmetric exponential power (AEP) distribution.
Computes the quantile function of AEP distribution given by [REMOVE_ME]FX−1(u∣Θ)=μ−σ(1−ϵ)[Γ(α1)γ(1−ϵ1−ϵ−2u,α1)]α1, u≤21−ϵ,[REMOVEME2]
[REMOVE_ME]FX−1(u∣Θ)=μ+σ(1+ϵ)[Γ(α1)γ(1+ϵ2u+ϵ−1,α1)]α1, u>21−ϵ.[REMOVEME2]
where −∞<x<+∞, Θ=(α,σ,μ,ϵ)T with 0<α≤2,σ>0, −∞<μ<∞, −1<ϵ<1, and [REMOVE_ME]γ(u,ν)=∫0utν−1exp{−t}dt, ν>0.[REMOVEME2]
Description
Computes the quantile function of AEP distribution given by
FX−1(u∣Θ)=μ−σ(1−ϵ)[Γ(α1)γ(1−ϵ1−ϵ−2u,α1)]α1, u≤21−ϵ,
FX−1(u∣Θ)=μ+σ(1+ϵ)[Γ(α1)γ(1+ϵ2u+ϵ−1,α1)]α1, u>21−ϵ.
where −∞<x<+∞, Θ=(α,σ,μ,ϵ)T with 0<α≤2,σ>0, −∞<μ<∞, −1<ϵ<1, and
γ(u,ν)=∫0utν−1exp{−t}dt, ν>0.
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.
Returns
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)