How are gamma-ray burst radio afterglows populated?

We systematically analyze three GRB samples named as radio-loud, radio-quiet and radio-none afterglows, respectively. It is shown that dichotomy of the radio-loud afterglows is not necessary. Interestingly, we find that the intrinsic durations ($T_{int}$), isotropic energies of prompt gamma-rays ($E_{\gamma, iso}$) and redshifts ($z$) of their host galaxies are log-normally distributed for both the radio-loud and radio-quiet samples except those GRBs without any radio detections. Based on the distinct distributions of $T_{int}$, $E_{\gamma, iso}$, the circum-burst medium density ($n$) and the isotropic equivalent energy of radio afterglows ($L_{\nu,p}$), we confirm that the GRB radio afterglows are really better to be divided into the dim and the bright types. However, it is noticeable that the distributions of flux densities ($F_{host}$) from host galaxies of both classes of radio afterglows are intrinsically quite similar. Meanwhile, we point out that the radio-none sample is also obviously different from the above two samples with radio afterglows observed, according to the cumulative frequency distributions of the $T_{int}$ and the $E_{\gamma, iso}$, together with correlations between $T_{int}$ and $z$. In addition, a positive correlation between $E_{\gamma, iso}$ and $L_{\nu,p}$ is found in the radio-loud samples especially for the supernova-associated GRBs. Besides, we also find this positive correlation in the radio-quiet sample. A negative correlation between $T_{int}$ and $z$ is confirmed to hold for the radio-quiet sample too. The dividing line between short and long GRBs in the rest frame is at $T_{int}\simeq$1 s. Consequently, we propose that the radio-loud, the radio-quiet and the radio-none GRBs could be originated from different progenitors.