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

Two classes of GRBs have been confidently identified thus far and are prescribed to different physical scenarios -- NS-NS or NS-BH 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 catalogs, such as BATSE and $Swift$, based on statistical tests regarding a mixture of two or three log-normal distributions of $T_{90}$. However, this might possibly not be an adequate model. This paper investigates whether the distributions of $\log T_{90}$ 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, existence of a third (intermediate) class of GRBs in $Fermi$ data is rejected, 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.