It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov’s theorem, we further investigate the analogous characteristic properties in terms of the sample mean and some feasible definite statistics. The latter statistics introduced in this paper for the first time are based on nonnegative, definite and continuous functions of ordered arguments with positive degree of homogeneity. The proposed approach seems to be natural and can be used to derive easily characterization results for many feasible definite statistics, such as known characterizations involving the sample variance, sample range as well as Gini’s mean difference.

众所周知，样本均值和样本方差的独立性表征了正态分布。通过使用阿诺索夫定理，我们进一步研究了样本均值和一些可行的确定统计量方面的类似特征属性。本文首次介绍的后一种统计是基于具有正齐次度的有序自变量的非负、定和连续函数。所提出的方法似乎是自然的，并且可以用于为许多可行的确定统计轻松导出表征结果，例如涉及样本方差、样本范围以及基尼平均差的已知表征。