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arXiv · 1209.6545

Modified frequentist determination of confidence intervals for Poisson distribution

S. I. Bitioukov·N. V. Krasnikov
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Abstract

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

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S. I. Bitioukov, N. V. Krasnikov. 2012-09-28. Modified frequentist determination of confidence intervals for Poisson distribution. https://doi.org/10.1134/s1063779613020081

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