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

Mixture models compose of a finite and infinite number of components that can describe several datasets. However, there are many situations in which mixed failure populations are encountered. Mixtures of distributions provide an important tool in modeling wide range of observed phenomena, which do not normally yield for modeling from classical distributions like normal, gamma, Poisson, binomial, etc. Applications of finite mixture models are in fisheries research, economics medicine, psychology, agriculture, life testing and reliability among others. Burr Type XII and Burr Type X distributions are very important and extensively used in many practical applications. Burr XII distribution is mainly used to explain the allocation of lifetime distributions as well as wealth distributions. Also, the Burr X distribution can be used quite effectively in modeling life time of random phenomena, health, agriculture and biology. The goal of the current thesis is to introduce a new mixture model from Burr Type XII and Burr Type X distributions. Some statistical properties of the mixture model are discussed. Methods of maximum likelihood and moments are proposed for estimating the parameters of mixture model in case of complete samples. Further, the maximum likelihood estimators are obtained based on Type II censored samples. A numerical study is implemented for investigating the accuracy of estimates for different sample sizes. The importance and flexibility of mixture model is assessed by applying it to real data sets and comparing it with other known mixture distributions

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