Distribution of gamma-ray bursts on the t90-hardness ratio plane and their classification revisited

TL;DR

This study analyzes gamma-ray burst data on the t90-hardness ratio plane using various statistical distributions and bootstrap methods, revealing that the classification into three classes is sample-dependent and possibly an artifact of small sample sizes.

Contribution

It introduces a comprehensive statistical approach with multiple distributions and bootstrap analysis to revisit gamma-ray burst classification, challenging the traditional three-class paradigm.

Findings

All samples fit symmetric distributions (Normal or Student).

Preference for three classes diminishes with larger sample sizes.

Small samples may falsely suggest an intermediate class.

Abstract

Using four mixed bivariate distributions (Normal distribution, Skew-Normal distribution, Student distribution, Skew-Student distribution) and bootstrap re-sampling analysis, we analyze the samples of CGRO/BATSE, Swift/BAT and Fermi/GBM gamma-ray bursts in detail on the t90-hardness ratio plane. The Bayesian information criterion is used to judge the goodness of fit for each sample, comprehensively. It is found that all the three samples show a symmetric (either normal or student) distribution. It is also found that the existence of three classes of gamma-ray bursts is preferred by the three samples, but the strength of this preference varies with the sample size: when the sample size of the data set is larger, the preference of three classes scheme becomes weaker. Therefore, the appearance of an intermediate class may be caused by a small sample size and the possibility that there are only two classes of gamma-ray bursts still cannot be expelled yet. A further bootstrap re-sampling analysis also confirms this result.