次序统计量的概率性质与统计应用

The Probability Properties and Statistical Applications of Order Statistics

摘要: 基于次序统计量在数理统计(非参数统计)中的重要应用，本文对次序统计量做了相对详细的介绍。本文给出了次序统计量的概念、性质，并通过离散型总体的案例说明了次序统计量的分布不同于随机样本(总体)的分布，且不具有独立性。不同于常见的微元法而运用分部积分法对次序统计量的分布密度作出了证明，并从可视化角度给出了常见连续型总体的次序统计量分布密度的数值分析与图像拟合。最后通过常用的非参数检验方法阐释了次序统计量在统计工作中的重要应用。

Abstract: Based on the important application of order statistics in mathematical statistics (nonparametric statistics), this paper introduces order statistics in detail. The concept and properties of order sta-tistics are given, and the distribution of order statistics is different from the distribution of random samples (population) and is not independent through the case of discrete populations. Different from the common microelement method, the partial integration method is used to prove the distribution density of the order statistic, and the numerical analysis and image fitting of the distribution density of the order statistic of the common continuous population are given from the visualization perspective. Finally, the important application of order statistics in statistical work is explained by commonly used nonparametric test methods.