On the Exact Distribution of a Normalized Ratio of the Weighted Geometric Mean to the Unweighted Arithmetic Mean in Samples From Gamma Distributions
推导了多个独立贝塔随机变量乘积的分布，并应用于伽马分布样本中加权几何均值与未加权算术均值之比的分布，给出了截断误差的上界，可用于统计假设检验。
Abstract The distribution of the product of several independent beta random variables as a mixture of beta distributions is derived by using a solution of Wilks's type B integral equation. This distribution is applied to finding the distribution of a normalized ratio of the weighted geometric mean (GM) to the unweighted arithmetic mean (AM) in random samples consisting of observations from gamma distributions, one observation being taken from each distribution. Two upper bounds for the truncation error related to the mixture representation are obtained. Application of these results to problems in testing statistical hypotheses is indicated.