Statistical Tools for Analyzing the Cosmic Ray Energy Spectrum
  In this paper un-binned statistical tools for analyzing the cosmic ray energy spectrum are developed and illustrated with a simulated data set. The methods are designed to extract accurate and precise model parameter estimators in the presence of statistical and systematic energy errors. Two robust methods are used to test for the presence of flux suppression at the highest energies: the Tail-Power statistic and a likelihood ratio test. Both tests give evidence of flux suppression in the simulated data. The tools presented can be generalized for use on any astrophysical data set where the power-law assumption is relevant and can be used to aid observational design. 
J. D. Hague, B. R. Becker, M. S. Gold, J. A. J. Matthews