Thesis (Ph.D.) - Cairo University - Institute of Statistical Studies and Research - Department of Mathematical Statistics

Statistical models are very useful in describing and predicting real-world phenomena. Numerous extended distributions have been extensively used over the last decades for modelling data in several areas. Recent developments focus on defining new families that extend well-known distributions and at the same time provide great flexibility in modelling data in practice. The goal of the current thesis is to introduce and study three new generated families of distributions, namely; exponentiated Weibull-G, Kumaraswamy Weibull-G and Type II half logistic-G. In the first family, the exponentiated Weibull distribution is taken as a generator while in the second family the Kumaraswamy Weibull distribution is taken as a generator. The odds ratio is to be taken as transformation in exponentiated Weibull-G and Kumaraswamy Weibull-G families. In third family, the half logistic is taken as a generator with another transformation. For each family, some statistical properties are derived and ML estimators are studied. 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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