TOPP-LEONE ZUBAIR GENERATED FAMILY OF DISTRIBUTIONS WITH APPLICATIONS TO LIFETIME DATA

Abstract

The Topp-Leone Zubair family of distribution was developed in this study to model life time data. This family of distributions is an improvement of the Topp-Leone and the Zubair families which lacked scale parameter and shape parameters respectively. The statistical properties of the generator were obtained , thus; mixture representation, moments, moment generating function, incomplete moments, inequality measures, mean deviation, median deviation, mean residual life, stochastic ordering, Stress strength, order statistics and the rth non-central moment. The method of estimations for the parameters of the generator was Maximum Likelihood estimation. Five new distributions have been developed from the family. These are: Topp-Leone Zubair Nadarajah Haghighi, Topp-Leone Zubair Lomax, Topp-Leone Zubair Weibull, Topp Leone Zubair Kumaraswamy and Topp-Leone Zubair Inverse Weibull. Further, the Topp-Leone Zubair Lomax regression model was developed and applied to censored data with independent factors. The simulation results showed that the average bias and the root mean square error of the estimators decrease as the sample size increases. Thus, the estimators passed the consistency test. The new models were also subjected to real life data and they were better than their competing models as per Kolmogorov Smirnov test, Bayesian Information criteria, Cramér-Von Mises, Akaike Information Criteria and that of Corrected Akaike Information Criteria. Histogram plots demonstrated a better fit of the new models on the respective data applied. It is recommended that the Topp-Leone Zubair family should be used to enhance the modeling performances of existing distributions that lack either shape or scale parameters.