Treatment of Errors in Efficiency Calculations

2007/01/17 by Tino Ullrich, T. Ullrich, Z. Xu +2 · 2 voices · 1 citation
Decision Sciences · Physics and Astronomy · #Data Analysis #FOS: Physical sciences #Probabilistic and Robust Engineering Design #Statistics and Probability (physics.data-an) #physics.data-an

paper · pdf · doi:10.48550/arxiv.physics/0701199

This paper has been withdrawn by the authors

openalex publication_date 2007/01/17 · arxiv published 2007/01/17 · arxiv created 2012/05/11 · arxiv updated 2012/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this report we discuss the treatment of statistical errors in cut efficiencies. The two commonly used methods for the calculation of the errors, Poissonian and Binomial, are shown to be defective. We derive the form of the underlying probability density function and characterize its mean, mode, and variance. A method for the calculation of errors based on the variance of the distribution is discussed.

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Discussions

• Your suggested paper proposes such extended square of variance, $$\sigma_\epsilon^2 = \frac{(\epsilon n+1)(\epsilon n+2)}{(n+2)(n+3)}-\frac{(\epsilon n+1)^2}{(n+2)^2},\tag 1$$ where $n=y_{total}$ , If [stackexchange, 4 points]
• First time posting here, so indulge with me if I do not respect yet the formatting. In the context of a particle physics work, I am studying the efficency of a detector. More precisely, its efficency [stackexchange, 4 points]

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