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arXiv 1209.6545physics.data-anhep-exhep-ph
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Poisson分布置信区间的修正频率论确定

Modified frequentist determination of confidence intervals for Poisson distribution

S. I. Bitioukov, N. V. Krasnikov

备注：
15 pages, 3 figures. Talk given by N.V. Krasnikov at Workshop "Calculations for modern and future colliders", Dubna, July 2012, Russia
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摘要：

我们提出了修改后的频率论定义的泊松统计的情况下的置信区间的确定。我们要求1-β ^β '} \geq \sum_{n=o}^{n_{obs}+k} P（n| λ）\geq α ^λ '}。我们证明了这个定义等价于先验为π（λ）\sim λ ^{k}的贝叶斯方法。其他的概括也被考虑。特别地，我们提出了修正的对称频率论定义，它对应于先验函数为π（λ）\sim 1/2（1 + \frac{n_{obs}} λ）的Bayes方法。提出了非零背景情况下的修正频率论定义。

英文摘要：

We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-β^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|λ) \geq α^{'}. We show that this definition is equivalent to the Bayesian method with prior π(λ) \sim λ^{k}. Other generalizations are also considered. In particular, we propose modified symmetric frequentist definition which corresponds to the Bayes approach with the prior function π(λ) \sim 1/2(1 + \frac{n_{obs}}λ). Modified frequentist definitions for the case of nonzero background are proposed.

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