• ON A CHARACTERIZATION OF THE EXPONENTIATED EXPONENTIAL DISTRIBUTIONBASED ON THE MINIMUM CHI-SQUARED DIVERGENCE PRINCIPLE

MAHMOUD ABD ALMO'MEN ATALLAH*, ABDULAZIZ ABD ULLAH ALQARNI

Abstract


Aprobability distribution can be characterized through various methods. Given a prior probability distribution g(x) and some available information on moments of the random variable X, the original probability distribution f(x) is determined such that the χ2- divergence measure of the distance between f(x) and g(x) is a minimum. The minimum chi-squared density function f(x) is determined. The expressions of the non-central moments as well as the cumulative distribution function F(x), survival function S(x), and hazard function h(x) are also determined under different available information on moments. In this paper we discussed the characterization of the Exponentiated exponential (EExp) distribution. The available information on moments included: first moment, second moment, the first two moments, and the first three moments. Some illustrative examples are included for special values of the parameters. We tabulated the results and the corresponding characteristics of the distribution are graphically, compared.


Keywords


Characterization, Exponentiated Exponential Distribution, Chi-square Divergence, Hazard Function, Available Information, Optimization Principle.

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