Possible correlations between gamma-ray burst and its host galaxy offset

We collected the information of 304 gamma-ray bursts (GRBs) from the literature, and analyzed the correlations among the host galaxy offsets (the distance from the site of the GRB to the center of its host galaxy), $T_{\rm 90,i}$(theduration$T_{\rm 90}$inrest-frame),$T_{\rm R45,i}$(theduration$T_{\rm R45}$inrest-frame),$E_{\rm \gamma,iso}$ (the isotropic equivalent energy), $L_{\gamma ,\mathrm{i}\mathrm{s}\mathrm{o}}$ ($=E_{\gamma ,\mathrm{i}\mathrm{s}\mathrm{o}}\mathrm{/}{T}_{90,\mathrm{i}}$, the isotropic equivalent luminosity) and $L_{\mathrm{p}\mathrm{k}}$ (peak luminosity). We found that $T_{90,\mathrm{i}}$, $T_{\mathrm{R}45,\mathrm{i}}$, $E_{\gamma ,\mathrm{i}\mathrm{s}\mathrm{o}}$, $L_{\mathrm{p}\mathrm{k}}$ have negative correlation with $\mathrm{o}\mathrm{f}\mathrm{f}\mathrm{s}\mathrm{e}\mathrm{t}$, which is consistent with origin of short GRBs (SGRBs) and long GRBs (LGRBs). On separate analysis, we found similar results for $\log E_{\gamma ,\mathrm{i}\mathrm{s}\mathrm{o}}$ - $\log (\mathrm{o}\mathrm{f}\mathrm{f}\mathrm{s}\mathrm{e}\mathrm{t})$ and $\log L_{\rm pk}$-$\log {\rm (offset)}$ relations in case of SGRBs only, while no obvious relation for LGRBs. There is no correlations between offset and $L_{\rm \gamma,iso}$. We also put the special GRB 170817A {and GRB 060218A} on the plots. {The two GRBs both have low luminosity and small offset.} In the $ \log ({\rm offset})- \log T_{\rm 90,i}$ plot, we found GRB 170817A locates in between the two regions of SGRBs and LGRBs and it is the outlier in the $ {\rm offset}-E_{\rm \gamma, iso}$,$ {\rm offset}-L_{\rm \gamma, iso}$and$ {\rm offset}-L_{\rm pk}$ plots. Together with GRB 060218A being an outlier in all plots, it indicates the speciality of GRBs 170817A and 060218A, and might imply more subgroups of the GRB samples.