Related papers: Power Laws and the Cosmic Ray Energy Spectrum
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…
The current measurements of the cosmic ray energy spectrum at ultra-high energies ($\text{E}>10^{19}$ eV) are characterized by large systematic errors and poor statistics. In addition, the experimental results of the two experiments with…
We study the angular power spectrum estimate in order to search for large scale anisotropies in the arrival directions distribution of the highest-energy cosmic rays. We show that this estimate can be performed even in the case of partial…
Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…
We report a measurement of the flux of cosmic rays with unprecedented precision and statistics using the Pierre Auger Observatory. Based on fluorescence observations in coincidence with at least one surface detector we derive a spectrum for…
Using data from the SUGAR and the AGASA experiments taken during a 10 yr period with nearly uniform exposure to the entire sky, we search for large-scale anisotropy patterns in the arrival directions of cosmic rays with energies > 10^{19.6}…
A common problem in ultra-high energy cosmic ray physics is the comparison of energy spectra. The question is whether the spectra from two experiments or two regions of the sky agree within their statistical and systematic uncertainties. We…
Seven and a half years of continuous monitoring of giant air showers triggered by ultra high-energy cosmic rays have been recently summarized by the AGASA collaboration. The resulting energy spectrum indicates clearly that the cosmic ray…
Energy-dependent patterns in the arrival directions of cosmic rays are searched for using data of the Pierre Auger Observatory. We investigate local regions around the highest-energy cosmic rays with $E \geq 6 \cdot 10^{19}$ eV by analyzing…
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…
We report on an observation of the difference between northern and southern skies of the ultrahigh energy cosmic ray energy spectrum with a significance of ${\sim}8\sigma$. We use measurements from the two largest…
We present results of numerical simulations of the propagation of ultra high energy cosmic rays (UHECRs) over cosmological distances, aimed at quantifying the statistical significance of the highest energy data on the spectrum and small…
Measurements of air showers are accumulating at an increasing rate while construction proceeds at the Pierre Auger Observatory. Although the southern site is only half complete, the cumulative exposure is already similar to those achieved…
Power-law cosmologies, in which the cosmological scale factor evolves as a power law in the age, $a \propto t^{\alpha}$ with $\alpha \ga 1$, regardless of the matter content or cosmological epoch, is comfortably concordant with a host of…
The high-energy non-thermal universe is dominated by power law-like spectra. Therefore results in high-energy astronomy are often reported as parameters of power law fits, or, in the case of a non-detection, as an upper limit assuming the…
Ultra-high energy cosmic rays impinging onto the atmosphere induce huge cascades of secondary particles. The measurement of the energy radiated by these air showers in form of radio waves enables an accurate measurement of the cosmic-ray…
Distances in cosmology are usually inferred from observed redshifts - an estimate that is dependent on the local peculiar motion - giving a distorted view of the three dimensional structure and affecting basic observables such as the…
We apply statistical inference on the Pierre Auger Open Data to discern for the first time the full mass composition of cosmic rays at different energies. Working with longitudinal electromagnetic profiles of cosmic ray showers, in…
Poisson distributed shot noise is normally considered in the Gaussian limit in cosmology. However, if the shot noise is large enough and the correlation function/power spectrum conspires, the Gaussian approximation mis-estimates the errors…
A formalism is presented that allows cosmological experiments to be tested for consistency, and allows a simple frequentist interpretation of the resulting significance levels. As an example of an application, this formalism is used to…