  Available in the literature are properties which characterize the gamma
distribution via independence of two appropriately chosen statistics.
Well-known is the classical result when one of the statistics is the sample
mean and the other one the sample coefficient of variation. In this paper, we
elaborate on a version of Anosov's theorem which allows to establish a general
result, Theorem 1, and a series of seven corollaries providing new
characterization results for gamma distributions. We keep the sample mean as
one of involved statistics, while now the second one can be taken from a quite
large class of homogeneous feasible definite statistics. It is relevant to
mention that there is an interesting parallel between the new characterization
results for gamma distributions and recent characterization results for the
normal distribution.
