Thesis (Ph.D.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Mathematical Statistics

Many statistical distributions have been extensively used and applied for modeling data in several areas such as engineering, actuarial, medical sciences, demography, etc. However, in many situations, the classical distributions are not suitable for describing and predicting real world phenomena. For that reason, attempts have been made to define new techniques for creating new distributions by introducing additional shape parameter(s) to baseline model and at the same time provide great flexibility in modeling data in practice. The extended distributions have attracted the attention of many authors to expand new models because the computational and analytical facilities available in programming software such as R, Maple, and Mathematica can easily tackle the problems involved in computing special functions in these extended distributions. The aim of this thesis is to introduce and study two new generated families of distributions, namely; the Kumaraswamy type I half logistic generated family of distributions and the type II Kumaraswamy half logistic generated family of distributions by taking the half logistic distribution as a generator for two families with different transformation for each one. Also, a new distribution "as deeply study case" is introduced, which is applied on the first family. Furthermore, some statistical properties are derived and maximum likelihood estimation is applied. Four sub models in each family are explored. Simulation study for a particular distribution in each family is performed. The importance and flexibility of each family is assessed by applying it to real data sets and comparing it with other known distributions

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