Testing the anisotropy in the angular distribution of $Fermi$/GBM gamma-ray bursts

Gamma-ray bursts (GRBs) were confirmed to be of extragalactic origin due to their isotropic angular distribution, combined with the fact that they exhibited an intensity distribution that deviated strongly from the $-3/2$ power law. This finding was later confirmed with the first redshift, equal to at least $z=0.835$, measured for GRB970508. Despite this result, the data from $CGRO$/BATSE and $Swift$/BAT indicate that long GRBs are indeed distributed isotropically, but the distribution of short GRBs is anisotropic. $Fermi$/GBM has detected 1669 GRBs up to date, and their sky distribution is examined in this paper. A number of statistical tests is applied: nearest neighbour analysis, fractal dimension, dipole and quadrupole moments of the distribution function decomposed into spherical harmonics, binomial test, and the two point angular correlation function. Monte Carlo benchmark testing of each test is performed in order to evaluate its reliability. It is found that short GRBs are distributed anisotropically on the sky, and long ones have an isotropic distribution. The probability that these results are not a chance occurence is equal to at least 99.98\% and 30.68\% for short and long GRBs, respectively. The cosmological context of this finding and its relation to large-scale structures is discussed.