Power Laws and the Cosmic Ray Energy Spectrum

Abstract

Two separate statistical tests are applied to the AGASA and preliminary 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. However, potentially large systematics on the relative energy scale prevent us from drawing definite conclusions at this time.

arXiv comment21 pages, 18 figures, submitted to Astro. Part. Phys

References in corpus (7)

• Power laws, Pareto distributions and Zipf's law
• Problems with Fitting to the Power-Law Distribution
• Extension of the Cosmic-Ray Energy Spectrum Beyond the Predicted Greisen-Zatsepin-Kuz'min Cutoff
• On the Frequency of Severe Terrorist Events
• New statistic for financial return distributions: power-law or exponential?
• Deviations of the distributions of seismic energies from the Gutenberg-Richter law
• The First Scientific Results from the Pierre Auger Observatory

Cited by in corpus (4)

• Observation of the suppression of the flux of cosmic rays above 4x10^19eV
• Measurement of the cosmic ray spectrum above $4\times 10^{18}$ eV using inclined events detected with the Pierre Auger Observatory
• Statistical Methods for Investigating the Cosmic Ray Energy Spectrum
• Statistical Tools for Analyzing the Cosmic Ray Energy Spectrum