The cosmic ray energy spectrum is well known to follow a power-law over many orders of magnitude. The question of whether the spectrum exhibits a cut-off is of primary importance. Following our Astro. Part. Phys. publication (astro-ph/0610865), we describe two statistical tests and apply them to the AGASA and preliminary (ICRC-2005) Auger Cosmic Ray Energy spectra in an attempt to find deviation from a pure power-law. The first test is constructed from the probability distribution for the maximum event of a sample drawn from a power-law. The second 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 AGASA data show no significant deviation from a power-law when subjected to both tests. Applying these tests to the Auger spectrum suggests deviation from a power-law. We also discuss the application of these tests to un-binned data thus showing a statistical advantage in un-binned verses binned analysis.

Proceedings of the 30th International Cosmic Ray Conference; Rogelio Caballero, Juan Carlos D'Olivo, Gustavo Medina-Tanco, Lukas Nellen, Federico A. Sánchez, José F. Valdés-Galicia (eds.); Universidad Nacional Autónoma de México, Mexico City, Mexico, 2008; Vol. 4 (HE part 1), pages 265-268