The Properties Of N Groups Shifted Nested 3-Samples Of Order Statistics

The distribution of order statistic is an important subject of probability theory. The distribution of n groups shifted nested 3-samples of order statistics is related to the multiple integral and the enumeration of Young tableaux in combinatorics.The paper considers the following nested multiple integral: In=?…?Dndx11dx12dx13…dx3n-2dx3n-1dx3n, hereThe results of In(n?6) are obtained and then the empirical formula is given byFinally, this empirical formula is proved by induction.