Distributions Of Two Nested Order Statistics Of Approximate C Shapes

Order statistics are a kind of frequently used statistics in probability theory and mathematical statistics.In this paper,we use the relation of nested order statistics and standard Young tableaux(SYT)to study some distribution problems of the nested order statistics by using multiple integrals,Euler's integrals and combinatorial identities.This paper mainly studies two categories of similar C-type of SYT-type charts which follow the uniform distribution on interval(0,1).According to the relationship between the nested order statistics of model and the SYT-type chart,firstly,the distribution on the nesting order statistics of the first SYT-type chart of(nm+2)\(n-k)\((n-1)m)|{(2,2)} is derived,which is subj ect to U(0,1).And then the closed formula of the number of SYT of the truncated shape(n3)\(n-k)\(n-1)| {(2,2)} is obtained.Finally,the distribution on nesting order statistics of the second SYT-type chart of(n3)\(n-k)\(n-2)| {(2,2)} is discussed,which complies with U(0,1).The representation of formulas corresponding to the three previous kinds of SYT-type charts are as follows,where Cm(k)=m/(k+m)(?)the relation of Catalan number:(?).