A STUDY ON BAYESIAN PREDICTION BASED ON SOME LIFE DISTRIBUTIONS

M.A.W.Mahmoud, Samia Saied El Azab ; Asmaa Ahmed Kamel Aly Saleh 


Abstract


Abstract Asmaa Ahmed Kamel Aly Saleh. A study on bayesian prediction based on some life distributions. Doctor of Philosophy of Science (Ph.D.) Dissertation of Pure Mathematics Faculty of women, Ain Shams University. In this thesis, the Bayesian prediction based on generalized ordered statistics samples for some useful distributions are considered. In the first part some basic concepts, historical surveys on some studies in theoretical and application which have been made on generalized order statistics and a description of all chapters are presented. The second part is concerned with the problem of the Bayesian one sample prediction of the generalized Pareto distribution based on generalized order statistic sample. The results are specialized to upper record values, upper ordinary order statistics and progressively type II censored samples. Finally, numerical results are obtained. The third part deals with Bayesian two-sample predictive for future observations from the generalized Pareto distribution based on generalized order statistics when the scale parameter σ is known and when the both parameters σ and θ are unknown. Two cases are considered fixed sample size and random sample size. The Bayesian prediction bounds for upper record values, ordinary order statistics and progressive type-II censoring as special cases of generalized order statistics are obtained. Finally, a Monte Carlo simulation study has been carried out to calculate the lower and the upper bounds of the future observation from ordinary order statistics, progressive type II censoring and upper record samples. In the fourth part, the Bayes estimation of unknown parameters from the generalized linear failure rate distribution is discussed based on generalized order statistics. Upper record values, ordinary order statistics and progressively Type-II censored as special cases of generalized order statistics are considered. Real data set was used for illustration and a Monte Carlo simulation study is carried out in order to compare the performance of different methods of obtained estimations. In the fifth part, based on a set of generalized order statistics from the generalized linear failure rate distribution, the problem of predicting the future generalized order statistics (one sample prediction scheme) using interval Bayesian prediction is discussed. The Bayesian prediction results are specialized to the cases upper record values, ordinary order statistics and progressive type-II censoring. Finally the lower and the upper bounds of the future observation are obtained using Lindley approximation and MCMC method based on a real ordinary ordered data set. The sixth part concerned with the problem of Bayesian two-sample prediction based on generalized order statistics from the generalized linear failure rate distribution. The Bayesian prediction results are specialized to the cases upper record values, ordinary order statistics and progressive type-II censoring. Finally, the lower and the upper predictive bounds of some observations are obtained using real ordinary ordered data set.


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Issue Date Jun-2016
URI http://research.asu.edu.eg/handle/123456789/2296


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