On The Strong Law Of Large Numbers For The Ratio Of Order Statistics In General Case

Order statistics and related knowledge play a vital role in many applications of statis-tics,and they are also widely used in production and life.In recent years,many scholars have increasingly studied the ratio of order statistics.And using it as the criterion for the stability of the local area.From the beginning of some specific distributions,such as the order statistics ratio of Pareto distribution,uniform distribution and exponential distribution,the conditions have become weaker and weaker and the research results are applied to more and more extensive fields.This paper first introduces the related background of order statistics and the current research results domestic and overseas and gives some important theorems.Secondly,the article briefly introduces some related knowledge about order statistics and the ratio of order statistics,as well as some definitions,theorems and properties needed for subsequent proofs.In the following part,the main theorem of this paper and its proof process are given,namely,the strong law of large numbers for the ratio of order statistics R_n23 and verify the strong law of large numbers that obey the exponential distribution and uniform distribution of the order statistics of the random variable sequence.Then,on the basis of Chapter 3,we give a generalization,that is,the strong law of large numbers for the ratio of any two adjacent order statistics R_ni(i+1) and the proof process.Finally,through summarizing the full paper,some thoughts and prospects are put forward on the existing research results.