Testing the Randomness in the Sky-Distribution of Gamma-Ray Bursts

We studied the complete randomness of the angular distribution of gamma-ray bursts (GRBs) detected by BATSE. Since GRBs seem to be a mixture of objects of different physical nature we divided the BATSE sample into 5 subsamples (short1, short2, intermediate, long1, long2) based on their durations and peak fluxes and 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 (9 from the Voronoi tesselation, 3 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 MC simulations enabled us to test the null hypothesis i.e. that the angular distributions are fully random. We tested the randomness by binomial test and introducing squared Euclidean distances in the parameter space of the test-variables. We concluded that the short1, short2 groups deviate significantly (99.90%, 99.98%) from the fully randomness in the distribution of the squared Euclidean distances but it is not the case at the long samples. At the intermediate group the squared Euclidean distances also give significant deviation (98.51%).