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We examined the properties of a sample of BATSE Gamma--Ray Bursts (GRBs) comprising events which have indications of association with a supernova (SN), some on the basis of indications of re--brightening in the optical afterglow light curve, but in most cases based only on the `loose' temporal and directional coincidence inferred from the cross correlation of catalogs. Despite of the large uncertainties in the latter selection method, the temporal and spectral analysis reveal three interesting statistical results when the sample is compared with that of all the BATSE GRBs: the GRBs tentatively associated with SNe are found to predominantly (in $\sim$ 80% of the cases) have single-peaked light curves, a softer spectrum (i.e. low energy power law index $\alpha \sim$ --1.5) and tend not to follow the Lag-Luminosity and Isotropic Energy--Peak Energy correlations. These three independent statistical properties point toward the existence of a significant number of under-luminous,GRB 980425-like events constituting -- at least from an observational point of view -- a tail or a separate class with respect to the whole of the BATSE GRB events. The unusually high percentage of SN Ibc among those identified by the catalog cross--correlation (factor $\sim 4$ higher than expected from SN catalog statistics) reinforces the non-randomness of (some of) the selected events

Gamma-ray bursts associated with supernovae: a systematic analysis of BATSE GRB candidates