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.

翻译：众所周知,样本平均值的独立性和样本差异是正常分布的特点。我们通过使用阿诺索夫的理论,进一步调查样本平均值和一些可行的明确统计数据的类似特征。本文首次介绍的后一种统计数据是基于具有正均度的定点参数的非消极、确定和连续功能。拟议方法似乎是自然的,可以用来为许多可行的明确统计数据,如已知的涉及样本差异的特征、样本范围以及吉尼的平均值等得出易于定性的结果。