关于离散型随机变量次序统计量分布矩阵对称性猜想的探索

Exploring Symmetry on Distribution Matrix of Order Statistics of Discrete Type Random Variable

本文研究了离散型随机变量次序统计量的分布矩阵的对称性 ,获得了二个定理 .定理 1 服从等概率二点分布或等概率三点分布的离散型随机变量的次序统计量的分布矩阵是对称矩阵 .定理 2 取值有限且等概率的离散型随机变量的次序统计量的分布矩阵具有中心对称性 .

In this paper, we study the symmetry on distribution matrix of order statistic of discrete type random variable. Therefore, we obtain two theorems. (i)If the discrete type random variable obey the equiprobability distribution of bipoint or tripoint, then their distribution matrix of order statistic is a symmetrical matrix. (ii)When the value of discrete type random variable is limited and obey the equiprobabilily distribution, then the distribution matrix of order statistic of discrete type random variable is central symmetric.