Statistical analysis of the Neumann-Pirson detection criterion for random quantities obeying a poisson distribution

Abstract

A numerical analysis of the confidence of detecting a significant deviation from the background distribution according to the Neumann-Pirson for random quantities, which obey the Poisson criterion, was performed. Relationships are established between such quantities as the signal-to-background ratio, the expected mean background value, the detection threshold, and the detection confidence. To completely define the problem, it is sufficient to know two of these four parameters. Because the distribution of events in each bin of a histogram at unit weights of events obey the Poisson distribution law, the obtained mutual dependences of variables are of fundamental importance and can be used in searches for a deviation from predictions of standard models or for a desired-signal detection against a background of known background distributions. The determined confidence values comply with the values that were obtained using the χ² method (Pirson criterion).