Some new Families of Continuous Distributions Generated from Burr XII Logit

Abstract

This thesis is based on six chapters. In these chapters five new families of distributions are introduced by using the Burr XII distribution. In Chapter 1, a brief introduction of the existing families of distribution, the objectives and organization of this thesis are presented. In Chapter 2, Generalized Burr G family of distributions is proposed by using the function of cdf ¡log[1 ¡ G(x)]. In Chapter 3, Marshall-Olkin Burr G family of distributions is introduced by using odd Burr G family of distributions used as generator proposed by Alizadeh et al. (2017). In chapter 4, odd Burr G Poisson family of distribution is introduced by compounding odd Burr G family with zero truncated Poisson distribution. In Chapter 5, a new generalized Burr distribution based on the quantile function following the method given by Aljarrah et al. (2014). In Chapter 6, Kumaraswamy odd Burr G family of distributions is introduced using odd Burr G family as a generator. The mathematical properties of these families are obtained, such as asymptotes and shapes, infinite mixture representation of the densities of the families, rth moment, sth incomplete moment, moment generating function, mean deviations, reliability and stochastic ordering, two entropies, Renyi and Shannon entropies. The explicit expression of distribution ith order statistic is also obtained in terms of linear combination of baseline densities and probability weighted moments. Model parameters are estimated by using the maximum likelihood (ML) method for complete and censored samples. Special models are given for each family, their plots of density and hazard rate functions are displayed. One special model for each family is investigated in detail. Simulation studies are also carried out to assess the validity of ML estimates of the model discussed in detail. Application on real life data is done to check the performance of the proposed families.