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.
