Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics

This thesis concentrates on the hypothesis testing and information criteria approaches for assessing the number of components in a nite mixture of Birnbaum-Saunders (BS) distributions. Initially, the identi ability for a g-component mixture of BS distributions is proved and the expectation{maximization (EM) algorithm is used to t the proposed model for random censoring data. Next, we propose the use of the EM test, the modi ed likelihood ratio test and the shortcut method of the bootstrap test for testing the number of components in the proposed model for random censoring data. Finally, we use several information criteria based on the likelihood and classi cation functions for selecting the number of components in the proposed model. Simulation studies, with a variety of scenarios, are provided to assess the performance of both hypothesis testing and information criteria approaches. In addition, real data sets are used to demonstrate the application of the proposed approaches

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