On Generalized Classes of Exponential Distribution using T-X Family Framework

Abstract

We introduce new generalized classes of exponential distribution, called T-exponentialfYg
class using the quantile functions of well-known distributions. We derive some general
mathematical properties of this class including explicit expressions for the quantile
function, Shannon entropy, moments and mean deviations. Some generalized exponential
families are investigated. The shapes of the models in these families can be
symmetric, left-skewed, right-skewed and reversed-J, and the hazard rate can be increasing,
decreasing, bathtub, upside-down bathtub, J and reverse-J shaped. Two real
data sets are used to illustrate the applicability of the new models.