Analysis of gamma-ray burst duration distribution using mixtures of skewed distributions

Abstract

Two classes of gamma-ray bursts (GRBs) have been confidently identified thus far and are prescribed to different physical scenarios-neutron star-neutron star or neutron star-black hole mergers, and collapse of massive stars, for short and long GRBs, respectively. A third, intermediate in duration class, was suggested to be present in previous catalogues, such as Burst Alert and Transient Source Explorer (BATSE) and Swift, based on statistical tests regarding a mixture of two or three lognormal distributions of T90. However, this might possibly not be an adequate model. This paper investigates whether the distributions of logT90 from BATSE, Swift, and Fermi are described better by a mixture of skewed distributions rather than standard Gaussians. Mixtures of standard normal, skew-normal, sinh-arcsinh and alpha-skew-normal distributions are fitted using a maximum likelihood method. The preferred model is chosen based on the Akaike information criterion. It is found that mixtures of two skew-normal or two sinh-arcsinh distributions are more likely to describe the observed duration distribution of Fermi than a mixture of three standard Gaussians, and that mixtures of two sinh-arcsinh or two skew-normal distributions are models competing with the conventional three-Gaussian in the case of BATSE and Swift. Based on statistical reasoning, and it is shown that other phenomenological models may describe the observed Fermi, BATSE, and Swift duration distributions at least as well as a mixture of standard normal distributions, and the existence of a third (intermediate) class of GRBs in Fermi data is rejected.