Topp Leone Exponential – G Family of Distributions: Properties and Application

Abstract

A new family of distributions called Topp leone Exponential-G family of
distributions is developed in this paper. Two sub-models from the family
of distributions are also developed; Topp leone Exponential-Exponential
(TLEE) and Topp leone Exponential Lomax (TLELx) distributions; their
respective density and distribution functions were shown. Some
structural properties of this new family of distributions were derived
such as moment, moment generating function, probability weighted
moment, Renyi entropy and order statistics. The parameters of the model
were estimated by using Maximum Likelihood Estimate (MLE) methods.
Finally, two real data sets were used to validate the results obtained
from MLE. The results showed that TLELx distribution provide a better
fit in the data sets than some other existing distributions. Perhaps, this
new family of distributions may be used to extend any other existing
probability models to modeling positive real data sets.