Document Details

Document Type : Thesis 
Document Title :
Recurrence Relations for Moments and Inferences Based on Generalized Order Statistics
علاقات تكرارية في العزوم واستدلالات على أساس الإحصاءات المرتبة المعممة
 
Subject : Girls' College of Education in Jeddah 
Document Language : Arabic 
Abstract : It is well known that there are many types of ordering the observations in statistics. Such observations can be obtained from scientific experiments, for example: ordinary order statistics, k-records, Pfeifer records, sequential order statistics, progressively type-II censoring samples with two stages and others. Kamps (1995) suggested a new theoretical technique called generalized order statistics (gos’s). This model contains all types of ordering mentioned above. In the last ten years, many researchers in the statistical studies used gos’s model in their research. The significance and importance of the present study are due to: • The great importance of the gos’s due to the important special cases included in this model. The use of general classes of continuous distributions including many probability distributions in addition to the doubly truncated distributions case. • The importance and applications of statistical Bayesian estimation and prediction in statistical medical and engineering studies, etc. Accordingly, the gos’s are used to find Bayesian estimates for parameters of some probability distributions, and Bayesian prediction intervals for some future observations. The present work has been organized and presented in six chapters. The results can be summarized as follows: Chapter one containts the current research-related studies were reviewed in addition to the presentation of statistical principles and the two classes of the continuous probability distributions considered in the present study. In chapter two some recurrence relations for joint moment generating functions and joint moments based on nonadjacent gos’s for the two classes in the doubly truncated case are derived. Recurrence relations for single and product moment generating functions and moments are also determined. These results are in concerned with the right and left truncated cases of the two classes. Some examples of the two classes have been illustrated to explain applications of the results. Some of the results in this chapter are accepted for publication (Ahmad and Abu-Shal (2006)) and some other have been submitted for publication. Chapter three presents recurrence relations for joint moment generating functions for the two classes of finite mixtures continuous distributions based on nonadjacent gos’s are derived. Also, recurrence relations for joint, single and product moment generating functions and moments for the two classes of finite mixtures continuous distributions are derived. Some examples of the two classes are given to illustrate the application of these results. In Chapter four the maximum likelihood and Bayes estimates of the parameters and functions of these parameters for one of the two classes under study using doubly type-II censoring gos’s are determined, these results are specialized to the oos’s and ourv’s. Some examples are presented in order to give numerical comparisons between maximum likelihood estimates and Bayes estimates for various parameters of distributions or functions of them. In chapter five Bayesian predictive survival function for a future sample of gos’s drawn from a class of continuous distributions given a doubly type-II censoring sample from the same class is derived. So, one can derive Bayesian prediction intervals for future observations (one-sample scheme). Bayesian prediction intervals for oos’s and ourv’s are obtained as special cases from gos’s. Two distributions of this class are studied to illustrate the use of Bayesian predictive survival function for finding the predictive interval limits for the future gos’s. Finally, chapter six discussed Bayesian prediction intervals for future observations from complete sample of gos’s which follow a class of continuous distributions given previous doubly type-II censoring sample of gos’s from the same class (two-sample scheme) are derived. Two distributions of this class are studied to illustrate the Bayesian prediction intervals for the future gos’s. Bayesian prediction intervals for medians of future samples with even or odd sizes, based on previous sample that explained earlier, have been obtained. 
Supervisor : dr. 
Thesis Type : Doctorate Thesis 
Publishing Year : 1430 AH
2009 AD 
Added Date : Wednesday, December 30, 2009 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
تهاني عبد الرحمن أبو شالAbushal, Tahani AbdulRahmanResearcherDoctorate 

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