Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical Research (FGSSR) - Department of Mathematical Statistics

Weighted distributions are suitable in the situations of unequal probability sampling, such as actuarial sciences, ecology, biomedicine, biostatistics and survival data analysis. It can be used in development of proper models for lifetime data,research related to reliability, econometrics, survey sampling and branching process. These distributions are applicable, when observations are recorded without any experiment, repetition and random process. The notion of weighted distributions has been used as a device for the collection of suitable model for observed data.The idea is most applicable when sampling frame is not available and random sampling is not possible.The exponentiated exponential and length-biased Lomax distributions are two important weighted distributions considered in the current thesis. Censoring is of great importance in planning duration experiments in reliability and lifetime studies whenever the experimenter does not observe the lifetimes of all test units. The traditional censoring schemes (Type I and Type II censoring) do not allow for units to be removed from the test at points other than the terminal point of the experiment. This allowance will be importantwhen a compromise between reduced time of experimentation and the observations of at least some extreme lifetimes are sought. When some of the surviving units in the experiment are removed early one can be used for some other experiments. This reason leads to the area of progressive censoring. In this thesis, based on progressively Type II censored samples, the maximum likelihood, Bayesian estimators of parameters, reliability and hazard functions of the exponentiated moment exponential and length-biased weighted Lomax distributions are derived.The asymptotic confidence intervals for parameters are discussed

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