Improved Asymptotic Formulae for Statistical Interpretation Based on Likelihood Ratio Tests

Abstract

In this work, we attempt to refine the classic asymptotic formulae to describe the probability distribution of likelihood-ratio statistical tests. The idea is to split the probability distribution function into two parts. One part is universal and described by the asymptotic formulae. The other part is case-dependent and is estimated explicitly using a 6-bin model proposed in this work. The latter is similar to performing toy simulations and can therefore predict the discrete structures in the probability distributions. The new asymptotic formulae provide a much better differential description of the test statistics. This improved performance is demonstrated in two toy examples for common likelihood ratio statistics.

version accepted for publication in Physica Scripta. Welcome to try it in your analysis and feedback. Thank you!

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