The Distributions Of (N~2)\{(1,k)} And (N~3)\{(1,k)} Type Nested Order Statistics With Applications

Order statistics are a kind of very important statistics in probability and statistics.In this paper,we obtain the distributions of(n2)\{(1,k)} and(n3)\{(1,k)} type nested order statistics by multiple integration methods,in which we let(nm)\{(1,k)}type nested order statistics be nested order statistics composing of m groups of n independent and identically distributed random variables with U(0,1)with the k th order statistic in the first group removed,that isFurthermore,the distributions of some special types—((2k)2)\(1,k+1)｝,((2k-1)3)\{(1,k)} and(n3)\{(1,n-1)} type nested order statistics also have been obtained in this paper.This article also discusses the applications of the distributions of these type nested order statistics in the enumerations of standard Young tableaux of corresponding truncated shapes and voting problems.