Abstract
ABSTRACT Using four mixed bivariate distributions (Normal distribution, Skew-Normal distribution, Student distribution, Skew-Student distribution) and bootstrap re-sampling analysis. We analyse the samples of CGRO/BATSE, Swift/BAT, and Fermi/GBM gamma-ray bursts in detail on the T90–HR (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.
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