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

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:

• Bimodality
• gamma-ray burst duration
• simulation
• skewness
• weighted distribution

AMS CLASSIFICATIONS:

• 60E05
• 62E15
• 97K80
• 85A35

Acknowledgments

Special thanks to Prof. Reinaldo Boris Arellano-Valle for introducing the excellent application, kindly help, and insightful comments and suggestions. The authors also would like thank the editor and the two anonymous referees for their constructive comments and suggestions, which helped us to improve earlier versions of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.