Some goodness of fit tests based on ranked set sample and cumulative distribution function /
Mohamed Soliman Abdallah
Some goodness of fit tests based on ranked set sample and cumulative distribution function / بعض اختبارات جودة التوفيبق تحت العينات المرتبة ودالة التوزيع التجميعى Mohamed Soliman Abdallah ; Supervised Samir Kamel Ashour - Cairo : Mohamed Soliman Abdallah , 2019 - 130 P. : charts ; 30cm
Thesis (Ph.D.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Mathematical Statistics
Ranked set sampling (RSS) have been widely accepted because of their excellent performance compared with many other famous sampling techniques. Thanks to the ranking information provided by either the unmeasured units or the auxiliary variable(s) or both, RSS is known to produce samples that are often much more representative to the interested population. Therefore a large amount of literature has fast grown on RSS and also more researches are expected in the near future. The most important factor has a significant effect on the performance of RSS is the quality ranking of the sampling items. As it is extensively investigated that if the assumption of the perfectness does not hold, RSS is known to be more efficient as if it had satisfied. Consequently, it is necessary to firstly examine the nature of the ranking process, so as to identify the effect of imperfect ranking on the efficiency of RSS. The main novelty of this dissertation is to place RSS at the heart of the academic researches through developing multifold new inferential procedures in the light of the missing data approach. The first problem is concerned with constructing a point estimation for cumulative distribution function (CDF). Our vision is to adopt the missing data mechanisms such as iterative EM algorithm and linear interpolation technique to develop new CDF estimators. The theoretical properties of these CDF estimators are considered. The second problem is testing the perfectness problem as it is shown that these proposed CDF estimators are quite helpful for creating new powerful tests
Concomitant variable EM algorithm Estimation methods
Some goodness of fit tests based on ranked set sample and cumulative distribution function / بعض اختبارات جودة التوفيبق تحت العينات المرتبة ودالة التوزيع التجميعى Mohamed Soliman Abdallah ; Supervised Samir Kamel Ashour - Cairo : Mohamed Soliman Abdallah , 2019 - 130 P. : charts ; 30cm
Thesis (Ph.D.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Mathematical Statistics
Ranked set sampling (RSS) have been widely accepted because of their excellent performance compared with many other famous sampling techniques. Thanks to the ranking information provided by either the unmeasured units or the auxiliary variable(s) or both, RSS is known to produce samples that are often much more representative to the interested population. Therefore a large amount of literature has fast grown on RSS and also more researches are expected in the near future. The most important factor has a significant effect on the performance of RSS is the quality ranking of the sampling items. As it is extensively investigated that if the assumption of the perfectness does not hold, RSS is known to be more efficient as if it had satisfied. Consequently, it is necessary to firstly examine the nature of the ranking process, so as to identify the effect of imperfect ranking on the efficiency of RSS. The main novelty of this dissertation is to place RSS at the heart of the academic researches through developing multifold new inferential procedures in the light of the missing data approach. The first problem is concerned with constructing a point estimation for cumulative distribution function (CDF). Our vision is to adopt the missing data mechanisms such as iterative EM algorithm and linear interpolation technique to develop new CDF estimators. The theoretical properties of these CDF estimators are considered. The second problem is testing the perfectness problem as it is shown that these proposed CDF estimators are quite helpful for creating new powerful tests
Concomitant variable EM algorithm Estimation methods