Using Gaussian Mixture Model (GMM) and expectation-maximization algorithm, we perform an analysis of time duration (T₉₀) for Compton Gamma Ray Observatory(CGRO)/BATSE, Swift/BAT and Fermi/GBM gamma-ray bursts (GRBs). The T₉₀ distributions of 298 redshift-known Swift/BAT GRBs have also been studied in both observer and rest frames. Bayesian information criterion has been used to compare between different GMM models. We find that two Gaussian components are better to describe the CGRO/BATSE and Fermi/GBM GRBs in the observer frame. Also, we caution that two groups are expected for the Swift/BAT bursts in the rest frame, which is consistent with some previous results. However, Swift GRBs in the observer frame seem to show a trimodal distribution, of which the superficial intermediate class may result from the selection effect of Swift/BAT.

In this work, we restudy the dependence of luminosity function and event rates for different gamma-ray burst samples on the criteria of sample selection and threshold effect. To compare with many previous studies, we have chosen two samples including 88 and 118 long bursts with known redshift and peak flux over 2.6 ph cm⁻² s⁻¹, from which 79 bursts are picked out to constitute our complete sample. It is found that the evolution of luminosity with redshift can be expressed by L∝(1 + z)^k with a diverse k relied more on the sample selection. Interestingly, the cumulative distributions of either non-evolving luminosities or redshifts are found to be also determined by the sample selection rather than the instrumental sensitivity. Nevertheless, the non-evolving luminosities of our samples are similarly distributed with a comparable break luminosity of L₀ ∼ 10⁵¹ erg s⁻¹. Importantly, we verify with a K-S test that three cases of event rates for the two burst samples evolve with redshift similarly except a small discrepancy due to sampling differences at low-redshift of z < 1, in which all event rates show an excess of Gaussian profile instead of monotonous decline no matter whether the sample is complete. Most importantly, it is found that the burst rates violate the star formation rate at low redshift, while both of them are good in agreement with each other in the higher-redshift regions as many authors discovered previously. Therefore, we predict that two types of long bursts are favored in terms of their associations with both the star formation and the cosmic metallicity.

We systematically compare the temporal and spectral properties of 53 supernova (SN)-associated and 15 kilonova (KN)-associated gamma-ray bursts (GRBs). We find that the spectral parameters of both types of GRBs are identically and lognormally distributed, consistent with those normal GRBs. The bolometric luminosities of SN/GRBs and KN/GRBs have a triple form, with the corresponding break luminosities of SN/GRBs are roughly two orders of magnitude larger than those of KN/GRBs. We build the power-law relations between the spectral lag and the luminosity of prompt γ-rays with indices of −1.43 ± 0.33 for SN/GRBs and −2.17 ± 0.57 for KN/GRBs in the laboratory frame, which are respectively coincident with the rest-frame values. We verify that both SN/GRBs and KN/GRBs comply with their own Amati relations that match those of long and short GRBs, respectively. Analysing X-ray afterglows with good plateau segments, we build the power-law relations between the X-ray luminosity and the plateau time with an index of −1.12 ± 0.17 for KN/GRBs and −1.08 ± 0.22 for SN/GRBs, which can be well explained by the relativistic shock driven by an energy injection. The plots of luminosity-lag, Amati relation, and luminosity-time show heavy overlap between the two types of GRBs, implying that they might share the same radiation mechanism despite originating from different progenitors or central engines.

We collect 133 fast radio bursts (FRBs), including 110 nonrepeating and 23 repeating ones, and systematically investigate their observational properties. To check the frequency dependence of FRB classifications, we define our samples with a central frequency below/above 1 GHz as subsample I/II. First, we find that there is a clear bimodal distribution of pulse width for subsample I. If we classify FRBs into short FRBs (sFRBs; 100 ms) as done for short and long gamma-ray bursts (GRBs), the sFRBs at higher central frequency are commonly shorter than those at lower central frequency not only for nonrepeating but also repeating sFRBs. Second, we find that fluence and peak flux density are correlated with a power-law relation of F ∝ S p , obs γ for both sFRBs and lFRBs whose distributions are obviously different. Third, the lFRBs with isotropic energies ranging from 10⁴² to 10⁴⁴ erg are more energetic than the sFRBs in the F–DM _EX plane, indicating that they are two representative types. Finally, it is interesting to note that the peak flux density behaves independently on the redshift when the distance of the FRBs becomes far enough, which is similar to the scenario of the peak flux evolving with redshift in the field of GRBs. We predict that fainter FRBs at a higher redshift of z > 2 can be successfully detected by FAST and the Square Kilometre Array in the near future.

Thanks to more and more gamma-ray bursts with measured redshift and extended emission detected by the recent space telescopes, it is urgent and possible to check whether those previous energy correlations still satisfy the particular sample involving only the bursts accompanied by tail radiations. Using 20 long and 22 short bursts with extended emission, we find that the popular γ -ray energy correlations of the intrinsic peak energy versus the isotropic energy (Amati relation) and the intrinsic peak energy versus the peak luminosity (Yonetoku relation) do exist in both short and long bursts. However, it is much better if these gamma-ray bursts with extended emissions are reclassified into two subgroups of E-I and E-II that make the above energy correlations more tight. As proposed by Zhang et al., the energy correlations can be utilized to distinguish these kinds of gamma-ray bursts in the plane of bolometric fluence versus peak energy as well. Interestingly, the peculiar short GRB 170817A belongs to the E-I group in the fluence versus peak energy plane, but it is an outlier of both the Amati and Yonetoku relations even though the off-axis effect has been corrected. Furthermore, we compare the radiation features between the extended emissions and the prompt gamma-rays in order to search for their possible connections. Taking into account all these factors, we conclude that gamma-ray bursts with extended emission are still required to model with dichotomic groups, namely E-I and E-II classes, which hint that they might have different origins.