Statistical Methods for Investigating the Cosmic Ray Energy Spectrum

TL;DR

This paper introduces two statistical tests for analyzing cosmic ray energy spectra, enabling researchers to assess deviations from power-law behavior and identify potential energy cut-offs in unbinned data.

Contribution

It develops and describes two novel statistical methods—the TP-statistic and a likelihood ratio test—for analyzing cosmic ray energy spectra.

Findings

TP-statistic effectively detects deviations from power-law

Likelihood ratio test identifies energy cut-offs

Methods are applicable to unbinned cosmic ray data

Abstract

Two separate statistical tests are described and developed in order to test un-binned data sets for adherence to the power-law form. The first test employs the TP-statistic, a function defined to deviate from zero when the sample deviates from the power-law form, regardless of the value of the power index. The second test employs a likelihood ratio test to reject a power-law background in favor of a model signal distribution with a cut-off.