Two Kinds Of Distributions And Applications Of Three Groups Of Hollow Nested Order Statistics

The research of order statistics plays an important role in probability theory and mathematical statistics.Some of its properties are independent of the distribution of maternal,so it easy to calculate,and therefore widely used.In this paper,nested order statistics are combined with standard Young tableau(SYT)to study the distribution of nested order statistics.This paper focuses on the distribution of the hollow nested order statistics from uniform distribution on interval(0,1),which is three groups of skew hollow type nested order statistics.The distribution of the nested order statistics is denoted as P?1.It's specific forms is:Using the multiple integral formula and the combinational number property,the numbers of three groups of skew hollow SYT-type charts is named as H?1.Then,according to the relationship between nested order statistics and SYT-type chart,we get the distribution of three groups of skew hollow nested order statistics:where,(?)Besides,we also study the distribution of three groups of right trapezoid hollow nested order statistics by using the same ways.It's distribution named as P?2,and it's SYT-type charts named as H?1.Then(?)where,(?)and(?)(the forth convolution of Catalan number).Finally,the distributions of these two types of hollow nested order statistics are applied to the voting problem.