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.

中文翻译：

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一类新的加权双峰分布与伽马暴持续时间数据的应用

迄今为止，伽马射线暴 (GRB) 已被可靠地识别出来，并被规定用于不同的物理场景、黑洞合并和大质量恒星的坍缩。GRBs持续时间的分布是GRBs的主要特征之一，呈双峰分布。因此，许多作者使用混合分布模型来拟合它们，这在经典或贝叶斯方法中都存在严重的估计问题。因此，在本文中，我们介绍了一类更灵活的加权双峰分布，称为 alpha 两片偏斜正态分布 (ATPSN)，用于对 GRB 持续时间数据集进行建模。讨论了分布的一些主要概率和推理特性，并进行了模拟研究以说明 MLE 的性能。