Limit Properties Of Order Statistics From Specific Distributions

As an important tool in modern statistical inference,order statistics play an irreplaceable role in both parametric and non-parametric statistical fields.There-fore,the research based on order statistics has important theoretical and practical significance.Further,we can understand the true meaning of random phenom-ena and find the law of random phenomena by studying the limit properties of order statistics.In this thesis,we study the limit properties of the difference of order statistics from Pareto distribution and the ratio of order statistics from exponential distribution.In the first part of this thesis,the limit properties of the difference of order statistics based on samples from Pareto distribution are investigated.When 1≤s<t=m,the first moment of the difference of order statistics D_istdo not exist.The proper weights and constant sequences are found for the difference of order statistics,and the strong law of large numbers is obtained by using the partition idea.We also give other limit theorems such as the complete convergence and the large deviation principle.When 1≤s<t=m-1,we obtain central limit theorem,the Marcinkiewicz-Zygmund law of large numbers,and almost sure central limit theorem for D_ist.In addition,we give the self-normalized moderate deviation principle and self-normalized law of the iterated logarithm.In the second part of this thesis,the limit properties of the ratio of order statistics based on samples from exponential distribution are investigated.When the sample size is fixed at m,we use truncation technology,convergence theorems and Markov inequality and other tools to obtain the complete convergence,the large deviation principle,the weak law of large numbers for R_i1tand on the basis of the weak law of large numbers,a limit theorem under two concrete sequences of positive real numbers for R_i1tis established.When the sample size tends to infinity,we give the weak law of large numbers for R_i12and on the basis of the weak law of large numbers,a limit theorem under two concrete sequences of positive real numbers for R_i12is established.The limit theorems established in this thesis have a certain significance for advancing the research of the difference of order statistics and the ratio of order statistics.