Applied Mathematics 2014, 4(2): 47-55 DOI: 10.5923/j.am.20140402.02 Statistical Properties of the Exponentiated Generalized Inverted Exponential Distribution Oguntunde P. E. 1,* , Adejumo A. O. 2 , Balogun O. S. 3 1 Department of Mathematics, Covenant University, Ota, Ogun State, Nigeria 2 Department of Statistics, University of Ilorin, Kwara State, Nigeria 3 Department of Statistics and Operations Research, Modibbo Adama University, Yola, Adamawa State, Nigeria Abstract We provide another generalization of the inverted exponential distribution which serves as a competitive model and an alternative to both the generalized inverse exponential distribution and the inverse exponential distribution. The model is positively skewed and its shape could be decreasing or unimodal (depending on its parameter values). The statistical properties of the proposed model are provided and the method of Maximum Likelihood Estimation (MLE) was proposed in estimating its parameters. Keywords Distributions, Estimation, Exponentiated, Generalization, Inverse Exponential, Positively Skewed 1. Introduction The Exponentiated distributions have been studied widely in statistics since 1995 and a number of authors have developed various classes of these distributions; Lemonte et al [1]. Mudholkar et al [2] introduced the Exponentiated Weibull distribution and since then, a number of authors have proposed and generalized many standard distributions based on the Exponentiated distributions. The Exponentiated Exponential distribution; Gupta and Kundu [3-5], The Exponentiated Gamma, Exponentiated Weibull, Exponentiated Gumbel and Exponentiated Frechet distributions; Nadarajah and Kotz [6], The Exponentiated Exponential-Geometric distribution; Silva et al [7], The Exponentiated Generalized Inverse Gaussian distribution Lemonte and Cordeiro [8], The Exponentiated Kumaraswamy distribution; Lemonte et al [1], The Exponentiated Inverted Weibull Distribution; Flaih et al [9] and the Exponentiated Generalized Inverse Weibull; Elbatal et al [10] distribution are examples of such in the literatures. The Exponentiated distribution is derived by raising the cumulative density function (cdf) of an arbitrary parent distribution to an additional non-negative parameter, say ' ' γ . According to Lemonte et al [1], the parameter ' ' γ characterizes the skewness, kurtosis and tails of the resulting distribution. Let X denote a random variable from an arbitrary parent distribution G, the cumulative density function (cdf) of the * Corresponding author: peluemman@yahoo.com (Oguntunde P. E.) Published online at http://journal.sapub.org/am Copyright © 2014 Scientific & Academic Publishing. All Rights Reserved resulting Exponentiated distribution is given by; () () Fx Gx γ = ; 0 γ > (1) where () Gx is the cdf of the parent distribution. The corresponding probability density function (pdf) is obtained by differentiating Equation (1) with respect to  to give; 1 () () () fx Gx gx γ γ − = (2) Where () () dG x gx dx = Once the cdf is obtained as in Equation (1), getting the pdf is quite simple; it only involves the knowledge of differentiation in calculus. On the other hand, Cordeiro et al [11] proposed a new class of distributions as an extension of the Exponentiated type distribution which can be widely applied in many areas of biology and engineering. Given a non-negative continuous random variable X, the cdf of the Exponentiated Generalized (EG) class of distribution is defined by; { } () 1 1 () Fx Gx β α   = − −     (3) where , 0 αβ > are additional shape parameters. It was noted in their research that the model in Equation (3) has a tractability advantage over the Beta Generalized family of distributions; Eugene et al [12] since Equation (3) does not involve any special function like the incomplete beta function. Equation (3) also has mild algebraic properties for simulation purposes because its quantile function takes a