论文标题
通过使用Anosov的定理，通过两个统计数据独立的伽马分布的新特征
New Characterizations of the Gamma Distribution via Independence of Two Statistics by Using Anosov's Theorem
论文作者
论文摘要
文献中可用的是通过两个适当选择的统计数据独立性来表征伽马分布的属性。众所周知，当统计数之一是样本平均值，另一个是样本变异系数时，经典结果。在本文中，我们详细介绍了Anosov定理的版本，该版本允许建立一个一般结果，定理1和一系列七个推论，为伽马分布提供了新的表征结果。我们将样本均值作为涉及的统计数据之一，而现在第二个可以从相当大的同质可行确定统计数据中获取。要提到的是，伽马分布的新表征结果与正态分布的最新表征结果之间存在有趣的相似之处。
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.
