The Distribution And Application Of The M-shifted Hollow Nested Order Statistics

The distribution of order statistic is an important subject in probability theory.The nested distribution of several groups of independent order statistics is related to the combinatorial mathematics of the number of standard Young tableaux.By using the number of standard Young tableaux of truncated shape of h_(m,n),this paper derives the distribution of nested order statistic of the shape Shifted hollow nested order statistic of the shape h_(m,n)consists of m groups of independent order statistics(?).Firstly,multiple integrals and combinatorial summations are used to evaluate numbers of SYT the truncated shapes h_(3,n),h_(4,n)and h_(5,n).And then distributions of nested order statistics can be respectively illustrated as:h_(3,n)=C(n)-1,h_(4,n)=C(n+1)-2n,h_(5,n)=C(n+2)-(2n²+3n-1).Where C(n)=1/(n+1)(?)is Catalan number.Furthermore,the distributions of nested order statistics h_(m,4)can be illustrated as:(?) Where F_m is Fibonacci number.At last,these nested order statistics are applied to the problem of voting.