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

Lifetime testing play an important role in industry and in many fields, and due to the high cost and the long time that the lifetime tests consume, statisticians developed a different types of censored samples, where the experimenter can terminate the experiment before all units are failed. There are many different types of censoring schemes as the conventional Type-I and Type-II censoring, the progressive censoring and many different types of censoring schemes will be discussed in the coming chapter. The main aim of this thesis is develop the methods of estimation and prediction to make a statistical inference for some lifetime distributions as Gompertz distribution and inverted Kumaraswamy distribution based on different types of censored samples. In Chapter 1, we give a brief introduction to the basic definitions of statistical inference and the probability lifetime distributions. Also an overview is proposed for different types of censored samples. In Chapter 2, we obtain the maximum likelihood (ML) and Bayesian estimators for the parameters of Gompertz distribution based on Type-II progressively hybrid censored samples. The one-sample Bayesian prediction intervals have been constructed. Also we obtained the sufficient and necessary condition for the existence and uniqueness of the MLEs

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