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

TL;DR

This study evaluates whether skewed distributions better model gamma-ray burst durations than traditional Gaussian mixtures, challenging the existence of an intermediate GRB class and proposing more accurate statistical representations.

Contribution

It introduces the use of skewed distributions for GRB duration modeling and demonstrates their superiority over Gaussian mixtures in describing observational data.

Findings

Skew-normal and sinh-arcsinh mixtures better fit Fermi data than three-Gaussian models.

Two skewed distributions can compete with three-Gaussian models for BATSE and Swift data.

Existence of a third intermediate GRB class is statistically rejected in Fermi data.

Abstract

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.