摘要翻译：
给出了n个独立的gamma分布随机变量Xi平方和的精确cdf的几种表示，特别是用一系列gamma分布函数。利用Laha对gamma分布的刻画，用Taylor级数方法导出了样本方差的精确分布，并以gamma分布为先导项。特别是对于整数阶α，还提供了一些级数，包括对于α=1和对于α>1几乎是这种类型的γ分布的凸组合。并用正交级数给出了(X1，...，Xn)与(1，...，1)的夹角π分布的一些表示。所有这些级数都基于相同的易于计算的cos(Phi)矩序列。
---
英文标题：
《Exact distribution of the sample variance from a gamma parent
  distribution》
---
作者：
Thomas Royen
---
最新提交年份：
2007
---
分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
--
一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--

---
英文摘要：
  Several representations of the exact cdf of the sum of squares of n independent gamma-distributed random variables Xi are given, in particular by a series of gamma distribution functions. Using a characterization of the gamma distribution by Laha, an expansion of the exact distribution of the sample variance is derived by a Taylor series approach with the former distribution as its leading term. In particular for integer orders alpha some further series are provided, including a convex combination of gamma distributions for alpha = 1 and nearly of this type for alpha > 1. Furthermore, some representations of the distribution of the angle Phi between (X1,...,Xn) and (1,...,1) are given by orthogonal series. All these series are based on the same sequence of easily computed moments of cos(Phi).
---
PDF链接：
https://arxiv.org/pdf/704.1415