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 <it>Swift</it>, based on statistical tests regarding a mixture of two or three lognormal distributions of <it>T</it><inf>90</inf>. However, this might possibly not be an adequate model. This paper investigates whether the distributions of log <it>T</it><inf>90</inf> from BATSE, <it>Swift</it>, and <it>Fermi</it> 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 <it>Fermi</it> 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 <it>Swift</it>. Based on statistical reasoning, and it is shown that other phenomenological models may describe the observed <it>Fermi</it>, BATSE, and <it>Swift</it> duration distributions at least as well as a mixture of standard normal distributions, and the existence of a third (intermediate) class of GRBs in <it>Fermi</it> data is rejected.