On the Generation of New Generalized Families and Classes of Lifetime Distributions with Applications

Abstract

This thesis is concerned with the construction and development of new families of distribu- tions including the Topp-Leone type II exponentiated half logistic-G family of distributions, the Topp-Leone exponentiated half logistic generalized-G family of distributions, the Topp-Leone-Gompertz-G power series class of distributions, the Marshall-Olkin-Topp-Leone-Gompertz-G family of distributions and the gamma odd power generalized Weibull-G family of distributions. Some mathematical and statistical properties of the new families of distributions are explored. The statistical properties studied include the expansion of the density function, hazard rate function and quantile function, moments, probability weighted moments, stochastic ordering, distribution of the order statistics and R´enyi entropy. The maximum likelihood technique is employed in the estimation of model parameters and Monte Carlo simulations are conducted to examine the consistency of the estimates considering average bias and root mean square errors. Applications using data sets from various disciplines are presented to demonstrate the importance and the applicability of these new families of distributions.