How common are long gamma-ray bursts in the local Universe?

The two closest gamma-ray bursts so far detected (GRBs 980425 and 060218) were both under-luminous, spectrally soft, long-duration bursts with smooth, single-peaked light curves. Only of the order of 100 GRBs have measured redshifts, and there are, for example, 2704 GRBs in the BATSE (Burst and Transient Source Experiment) catalogue alone. It is therefore plausible that other nearby GRBs have been observed but not identified as being relatively nearby. Here we search for statistical correlations between BATSE long-duration GRBs and galaxy samples with recession velocities v <= 11 000 km s(-1) (z = 0.0367, approximate to 155 Mpc) selected from two catalogues of nearby galaxies. We also examine the correlations using burst subsamples restricted to those with properties similar to the two known nearby bursts. Our results show correlation of the entire long-GRB sample to remain consistent with zero out to the highest radii considered whereas a subsample selected to be low fluence, spectrally soft, with smooth single-peaked light curves (177 bursts), demonstrates increased correlation with galaxies within approximate to 155 Mpc. The measured correlation (28 +/- 16 per cent of the sample) suggests that BATSE observed between two and nine long-duration GRBs per year similar to, and from within similar distances to, GRBs 980425 and 060218. This implies an observed local rate density (to BATSE limits) of 700 +/- 360 Gpc(-3) yr(-1) within 155 Mpc