2008/06/24 by R. Vavrek, L. G. Balázs, A. Mészáros +2 · 5 citations
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Euclidean geometry #Gamma-ray bursts and supernovae #Monte Carlo method #Multifractal system #Randomness #Scientific Research and Discoveries #Statistical hypothesis testing #Test statistic #Voronoi diagram #astro-ph
paper · pdf · doi:10.1111/j.1365-2966.2008.13635.x
17 pages, 4 figures, accepted for publication in MNRAS
arxiv created 2008/06/24 · openalex publication_date 2008/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We have studied the complete randomness of the angular distribution of gamma-ray bursts (GRBs) detected by the Burst and Transient Source Experiment (BATSE). Because GRBs seem to be a mixture of objects of different physical nature, we divided the BATSE sample into five subsamples (short1, short2, intermediate, long1, long2) based on their durations and peak fluxes, and we studied the angular distributions separately. We used three methods, Voronoi tesselation, minimal spanning tree and multifractal spectra, to search for non-randomness in the subsamples. To investigate the eventual non-randomness in the subsamples, we defined 13 test variables (nine from the Voronoi tesselation, three from the minimal spanning tree and one from the multifractal spectrum). Assuming that the point patterns obtained from the BATSE subsamples are fully random, we made Monte Carlo simulations taking into account the BATSE's sky-exposure function. The Monte Carlo simulations enabled us to test the null hypothesis (i.e. that the angular distributions are fully random). We tested the randomness using a binomial test and by introducing squared Euclidean distances in the parameter space of the test variables. We concluded that the short1 and short2 groups deviate significantly (99.90 and 99.98 per cent, respectively) from the full randomness in the distribution of the squared Euclidean distances; however, this is not the case for the long samples. For the intermediate group, the squared Euclidean distances also give a significant deviation (98.51 per cent).