  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.
