The T-Exponentiated Exponential{Frechet} Family of Distributions: Theory and Applications
Conleth Chinazom Odom *
Department of Mathematics and Statistics, University of Port Harcourt, Nigeria.
Ethelbert Chinaka Nduka
Department of Mathematics and Statistics, University of Port Harcourt, Nigeria.
Maxwell Azubuike Ijomah
Department of Mathematics and Statistics, University of Port Harcourt, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This article introduces a new family of Generalized Exponentiated Exponential distribution. Using the T-R{Y} framework, a new family of T-Exponentiated Exponential{Y} distributions named T-Exponentiated Exponential{Frechet} family of distributions is proposed. Some general properties of the family such as hazard rate function, quantile function, non-central moment, mode, mean absolute deviations and Shannon’s entropy are discussed. A new continuous univariate probability distribution which is a member of the T-Exponentiated Exponential{Frechet} family of distributions is introduced. From the general properties of the family, expressions are derived for some specific properties of the new distribution. To show the usefulness of the T-Exponentiated Exponential{Frechet} family of distributions, the new distribution is fitted to two real life data sets and the results are compared with the results of some other existing distributions.
Keywords: Exponentiated-exponential distribution, T-R{Y} framework, moments, Quantile function, generalized distribution