三段式嵌套顺序统计量的分布及应用  

The Distribution and Application of Three-Stage Nested Order Statistics

作　　者：樊湉航 孙平[1] FAN Tianhang;SUN Ping(College of Science,Northeastern University,Shenyang 110000,China)

机构地区：[1]东北大学理学院,辽宁沈阳110000

出　　处：《许昌学院学报》2024年第5期19-24,共6页Journal of Xuchang University

摘　　要：顺序统计量在非参数统计分析中有着广泛的应用,嵌套顺序统计量的分布则依赖于具体的嵌套结构以及随机变量的分布特性.在研究三段式嵌套顺序统计量的分布时,可以将问题转化为嵌套积分,通过对相应的嵌套单形进行多重积分得到三段式嵌套顺序统计量的分布.这种分析方法的应用十分广泛,由于Standard Young Tableaux (SYT)的每一行对应一组独立的顺序统计量,因此文章将其应用于SYT的计数问题.此外,文章还将三段式嵌套顺序统计量的分布应用于选票问题.Order statistics are extensively applied in nonparametric statistical analysis,while the distribution of nested order statistics depends on the specific nested structure and the distribution characteristics of random variables.When studying the distribution of the three-stage nested order statistics,the problem can be converted into nested integrals,and the distribution can be derived by performing multiple integrals on the corresponding nested simplex.This analytical approach finds widespread application.Given that each row of the Standard Young Tableaux(SYT) corresponds to a set of independent order statistics,the method is applied to the counting problem of SYT.Additionally,the distribution of three-stage nested order statistics is also applied to the issue of vote counting.

关 键 词：顺序统计量 多重积分 Standard Young Tableaux 

分 类 号：G434[文化科学—教育学]