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 (T$_{90}$ 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 knn() k-nearest neighbour algorithm in the FNN library of the R statistical package. 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 the lda() in MASS library of R. To get the strength of the relationship between the parameters obtained from the GBM and BAT, a canonical correlation was performed using the cc() procedure in the CCA library in R. The GBM and BAT T$_{90}$ 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.