Some Limit Behavior For Linear Combinations Of Order Statistics

With the progress of science and the development of the society,more and more ran-dom phenomena have become the focus of scientific research,and probability statistics,as a research tool,has been paid more and more attention.Probability limit theory,the theoretical basis of subject is more important in probability and statistics,it is of great im-portance to study the asymptotic properties of linear combinations of order statistics.The first chapter mainly introduces the research background of this dissertation,the meaning of this dissertation and the main research content of this dissertation,at the same time,we introduce the main model we need to study.In order to illustrate the main research content of this paper better,in the second chapter,we introduce some knowledge of probability theory,such as the law of large num-bers,the central limit theorem,the large deviation principle,etc.Finally,some common lemmas of probability theory are given to prove the main conclusions of this paperIn the third chapter,the main conclusions and the proof process of this dissertation are given.For the linear combination of order statistics,the middle deviation and large deviation principles are studied respectively,moreover,we generalize the linear combination of order statistics.In the case of selecting appropriate coefficient,we prove that the error rate of the linear combination of order statistics converge to the normal distribution is O(n-1/2),and obtain its convergence rate,and further get the Cramer moderate deviation results.As applications,the moderate and large deviations for the k-th order statistics from uniform distribution and general continuous distribution are obtained respectively.