A new class of weighted bimodal distribution with application to gamma-ray burst duration data

Najme Sharifipanah; Rahim Chinipardaz; Gholam Ali Parham

doi:10.1080/02664763.2020.1815669

A new class of weighted bimodal distribution with application to gamma-ray burst duration data

J Appl Stat. 2020 Sep 4;47(13-15):2785-2807. doi: 10.1080/02664763.2020.1815669. eCollection 2020.

Authors

Najme Sharifipanah¹, Rahim Chinipardaz¹, Gholam Ali Parham¹

Affiliation

¹ Faculty of Mathematical Sciences and Computer, Department of Statistics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

Abstract

Gamma-ray bursts (GRBs) have been confidently identified thus far and are prescribed to different physical scenarios, black hole mergers, and collapse of massive stars. The distribution of GRBs duration, which is one of the main characteristics of GRBs, is bimodal. Hence, many authors have used mixtures of distribution models to fit them, which suffers serious estimation problems either from classical or Bayesian approaches. Therefore, in this article we introduced a more flexible class of weighted bimodal distribution, called alpha two-piece skew normal (ATPSN), for modeling GRBs duration data set. Some of the main probabilistic and inferential properties of the distribution are discussed and a simulation study is carried out to illustrate the performance of the MLEs.

Keywords: 60E05; 62E15; 85A35; 97K80; Bimodality; gamma-ray burst duration; simulation; skewness; weighted distribution.