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摘要翻译：
从密度不一定相同的独立实随机变量半正定二次型的Laplace变换的适当积分表示出发，导出了I.I.D.样本方差累积分布函数的一元积分表示。具有γ密度的随机变量，补充了作者以前的公式。进一步，由上述拉普拉斯变换得到了I.I.D.的密度和样本方差分布函数的Fourier级数。均匀分布的随机变量。该分布可应用于例如对标度参数的统计检验。
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英文标题：
《On the Laplace transform of some quadratic forms and the exact
distribution of the sample variance from a gamma or uniform parent
distribution》
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作者：
T. Royen
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最新提交年份：
2007
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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
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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。
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英文摘要：
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for the cumulative distribution function of the sample variance of i.i.d. random variables with a gamma density, supplementing former formulas of the author. Furthermore, from the above Laplace transform Fourier series are obtained for the density and the distribution function of the sample variance of i.i.d. random variables with a uniform distribution. This distribution can be applied e.g. to a statistical test for a scale parameter.
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PDF链接：
https://arxiv.org/pdf/710.5749
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