fitaep {AEP} R Documentation

## Estimating the parameters of AEP distribution through the expectation-maximization (EM) algorithm

### Description

Estimates the parameters of AEP distribution for which the pdf is given by

f_{X}(x|Θ)=≤ft\{\begin{array}{*{20}c} \frac{1}{2σ Γ\bigl(1+\frac{1}{α}\bigr)}\exp\biggl\{-\bigg|\frac{μ-x}{σ(1-ε)}\bigg|^{α}\biggr\},~~~x ≤q μ,\\ \frac{1}{2σ Γ\bigl(1+\frac{1}{α}\bigr)}\exp\biggl\{-\bigg|\frac{x-μ}{σ(1+ε)}\bigg|^{α}\biggr\},~~~x>μ, \end{array} \right.

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

### Usage

fitaep(x, initial = FALSE, starts)

### Arguments

 x Vector of observations. initial By default is FALSE. If the initial values are given by user, then set initial=TRUE. starts If initial values are not given by user, i.e., initial=FALSE, then vector starts must contain the initial values of the parameter vector, i.e., starts=\bigl(α^{(0)}, σ^{(0)}, μ^{(0)}, ε^{(0)} \bigr) for starting the EM algorithm.

### Value

A list of objects in two parts as

1. The EM estimator for the parameters of AEP distribution.

2. A sequence of goodness-of-fit measures consist of Akaike Information Criterion (AIC), Consistent Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC), Hannan-Quinn information criterion (HQIC), Anderson-Darling (AD), Cram\'eer-von Misses (CVM), Kolmogorov-Smirnov (KS), and log-likelihood (log-likelihood) statistics.

Mahdi Teimouri

### References

A. P. Dempster, N. M. Laird, and D. B. Rubin, 1977. Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society Series B, 39, 1-38.

### Examples

x <- raep(n=50, alpha=.8, sigma=1, mu=0, epsilon=0.5)
fitaep(x, initial = FALSE, starts)


[Package AEP version 0.1.2 Index]