Distribution Of The Hollow Nested Order Statistics Of The Shape Of Approximately Q

Order statistics,widely used in many fields,is one of the most important statistics in probability statistics.In this paper,the probability distribution of hollow nested order statistics of Young tableaux type is studied by combining the nested order statistics with the knowledge of combinatorial mathematics.In this paper,the order statistics of shape((n+2)m+1,n+1)\(nm-1,n-1)|{(2,2)},(n,m≥2)is a hollow nested order statistics composed of m+2 independent order statistics that obey U(0,1)distribution.By applying nested order statistics,calculating multiple integrals and using properties of combinatorial mathematics,the enumeration of the SYT-type charts of shape((n+2)m+1,n+1)\(nm-1,n-1)|{(2,2)},(n,m≥2)is obtained,whose result is a complex double combination equation.The corresponding probability distribution is further obtained,that is recorded as P((n+2)m+1,n+1)\(nm-1,n-1)|(2,2)}·By giving the value n in the probability distribution,we directly obtain the probability distribution of the hollow nested order statistics of shape(5m+1,4)\(3m-1,2)|{(2,2)},(m≥2)that is derived as follows:...