A STUDY ON BAYESIAN PREDICTION BASED ON SOME LIFE DISTRIBUTIONS

Abstract

Prediction problems arise in many real life situations. Various disciplines in which prediction finds importance are medicine, engineering, and business, among others. In the context of reliability theory, one may be interested in predicting the time to the next failure (one sample prediction) or in predicting the failure times in a new experiment (two sample prediction). Statistical prediction uses data from an informative experiment in order to make some statement about the future outcome. The main aim of this thesis is to study the problem of Bayesian prediction from the generalized Pareto distribution and the generalized linear failure rate distribution based on generalized order statistic samples. The thesis consists of six chapters Chapter 1:it contains some basic concepts which will be used throughout this thesis. The historical surveys on some studies in theoretical and application which have been made on generalized order statistics are also presented. Finally, it contains a description of all chapters of this thesis. Chapter 2is 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. Chapter 3deals with Bayesian predictive intervals for future observations from the generalized Pareto distribution based on generalized order statistics are obtained when the scale parameter σ is known and when the both parameters σ and θ are unknown. Two cases are considered: (i) fixed sample size (FSS), and (ii) random sample size (RSS). 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.