Document Details

Document Type : Thesis 
Document Title :
Thery of bootstrapping exteme order statistics with some application
نظرية اليوتستراب للاحصاءات المركبة المتطرفة مع بعض التطبيقات
 
Subject : Sciences Faculty for Girls - Department of Mathematics 
Document Language : Arabic 
Abstract : The purpose of this thesis to find the confidence intervals for the upper and lower endpoints for bootstrap distribution under power normalization constants by simulation. This require a general study of order statistics, the extreme value, convergence and consistency. So we have presented comprehensive study of bootstrap which is one of the most important method in statistical inference. It was known since 1970, and it has many applications such as estimation of variance and confidence intervals. We have focused on confidence interval. In Chapter one we have reviewed quickly the Asymptotic theory which plays an important role in the study of order statistics, because of the difficulty of numerical calculation of its distributions and strong dependent on society distribution which is unknown for researchers in many cases. After that we have discussed the extreme value theory and studied the distributions of order statistics and their properties. In Chapter two, we have discussed the bootstrap method which depends in its calculations on specific programs in the computer. the bootstrap word means statistically generation of data by drawing with replacement of the original data to estimate the parameters of society at a higher resolution than the known estimation methods. The bootstrap estimating for standard error and its algorithm were discussed. A comparison between Jackknife method and bootstrap method was presented. The bootstrap method was studied in details through construction of nonparametric confidence intervals for real parameter. In practice, construction of this intervals requires the simulation of Monte Carlo for a large number of a repeated bootstrap. Most of common bootstrap methods derive confidence boundaries from middle order statistics based on frequency of sample B. In third Chapter, we have studied the bootstrap method of extreme value under liner normalization constants, and we found confidence intervals of endpoints of cumulative distribution function. Then we have studied an application to find confidence intervals of endpoints and confidence intervals of bootstrap and compare the results through tables at different values. In Chapter four, the bootstrap theory of extreme distribution under power normalization constants was studied when the main distribution belongs to a domain attraction for extreme values distribution. In 2006 Nigm had studied the properties of bootstrap distribution such as inconsistency, weak consistency and strong consistency in the case of suitable selection of sample size at resample and when power normalization constants are known. And he studied The bootstrap theory of common probability distribution theoretically , and found that confidence intervals of the upper limit points of the distribution function W(f). The researcher has studied in this chapter a case by simulation to find confidence intervals for upper limit points and lower limit points of bootstrap distribution under power normalization constants, and the study is based on the families of distributions which are belongs to distributions under power normalization constants. 
Supervisor : porf.El Sayed Mahsoub Nigm 
Thesis Type : Doctorate Thesis 
Publishing Year : 1433 AH
2012 AD 
Added Date : Wednesday, July 11, 2012 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
فايزة طالع الحربيALHRBAI, Faiza TResearcherDoctorate 

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