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The two-point angular correlation function is a traditional method used to search for deviations from expectations of isotropy. In this paper we develop and explore a statistically descriptive three-point method with the intended application being the search for deviations from isotropy in the highest energy cosmic rays. We compare the sensitivity of a two-point method and a shape-strength method for a variety of Monte-Carlo simulated anisotropic signals. Studies are done with anisotropic source signals diluted by an isotropic background. Type I and II errors for rejecting the hypothesis of isotropic cosmic ray arrival directions are evaluated for four different event sample sizes: 27, 40, 60 and 80 events, consistent with near term data expectations from the Pierre Auger Observatory. In all cases the ability to reject the isotropic hypothesis improves with event size and with the fraction of anisotropic signal. While ~40 event data sets should be sufficient for reliable identification of anisotropy in cases of rather extreme (highly anisotropic) data, much larger data sets are suggested for reliable identification of more subtle anisotropies. The shape-strength method consistently performs better than the two point method and can be easily adapted to an arbitrary experimental exposure on the celestial sphere.
The main objective of the Cosmic-Ray Extremely Distributed Observatory (CREDO) is the detection and analysis of extended cosmic ray phenomena, so-called super-preshowers (SPS), using existing as well as new infrastructure (cosmic-ray observatories, e
The Galactic magnetic field, locally observed to be on the order of a few $mu$G, is sufficiently strong to induce deflections in the arrival directions of ultra-high energy cosmic rays. We present a method that establishes measures of self-consistenc
Higher-order, non-Gaussian aspects of the large-scale structure carry valuable information on structure formation and cosmology, which is complementary to second-order statistics. In this work we measure second- and third-order weak-lensing aperture-
We propose a new pattern-matching algorithm for matching CCD images to a stellar catalogue based statistical method in this paper. The method of constructing star pairs can greatly reduce the computational complexity compared with the triangle method