الفهرس 
IntroductionOnly 14 pages are availabe for public view
 |  | from | 157 |  |  |
| | | from | 157 | | |
Abstract
[Epstein, 1954] discussed a hybrid censoring scheme as a mixture of Type-I and Type- II censoring schemes, these schemes have been used in practice. However, these censoring schemes have some disadvantages. To avoid these disadvantages, [Chan- drasekar et al., 2004] proposed two new schemes which are called generalized Type-I and Type-II hybrid censoring scheme. To avoid the drawbacks in these schemes, [Bal- akrishnan et al., 2008] introduced a mixture of generalized Type-I and Type-II hybrid censoring scheme which is called the unified hybrid censoring scheme.
The main aim of this thesis is to obtain statistical estimation and prediction for the exponentiated Rayleigh distribution based on unified hybrid censoring data. The thesis consists of three chapters.
In Chapter 1, we present some basic concepts which will be used throughout this the- sis. Also, we show a historical survey on some studies in theoretical and application which have been made on exponentiated Rayleigh distribution since its formulation until the latest issued researches. Finally, it contains a description of under-study prob- lem.
In Chapter 2, the maximum likelihood estimation, the approximate confidence in- tervals and constructing the bootstrap confidence intervals procedure from exponenti- ated Rayleigh distribution based on unified hybrid censoring data are discussed. Also, Markov chain Monte Carlo technique and Lindley’s approximation are used for com- puting the Bayes estimation under three different loss functions and three different balanced loss functions from ER distribution based on unified hybrid censoring data. A real data and simulation data sets are used for illustration the theoretical results. The results of this chapter have been published in ”Journal of Advances in Mathematics” [Ghazal and Hasaballah, 2017 a] and in ”Journal of Statistics Applications & Proba- bility” [Ghazal and Hasaballah, 2017 b].
In Chapter 3, one- and two-sample Bayesian prediction intervals based on unified hybrid censoring data from the ER distribution are obtained. A real data set is used to compare the results obtained by MCMC technique. The results of this chapter have been submitted for publication in ”Journal of Statistical Computation and Simu- lation”[Ghazal and Hasaballah, 2017 c]