Some statistical remarks on GRBs jointly detected by Fermi and Swift satellites

Abstract

We made statistical analysis of the Fermi GBM and Swift BAT observational material, accumulated over 15 years. We studied how GRB parameters (T90 duration, fluence, peak flux) that were observed by only one satellite differ from those observed by both. In the latter case, it was possible to directly compare the values of the parameters that both satellites measured. The GRBs measured by both satellites were identified using the k-nearest neighbours algorithm in Euclidean distance. In the parameter space we determined the direction in which the jointly detected GRBs differ most from those detected by only one of the instruments using linear discriminant analyses. To get the strength of the relationship between the parameters obtained from the GBM and BAT, a canonical correlation was performed. The GBM and BAT T90 distributions were fitted with a linear combination of lognormal functions. The optimal number of such functions required for fit is two for GBM and three for BAT. Contrary to the widely accepted view, we found that the number of lognormal functions required for fitting the observed distribution of GRB durations does not allow us to deduce the number of central engine types responsible for GRBs.