Aims: Taking advantage of the forthcoming Catalog of the HETE-2 mission, the aim of this paper is to evaluate the main properties of HETE-2 GRBs - the E_peak, the T_90 and the E_iso - in their source frames and to derive their unbiased distribution.
Methods: We first construct a complete sample containing all the bursts localized by the WXM on-board HETE-2, which are selected with a uniform criterion and whose observed parameters can be constrained. We then derive the intrinsic E_peak, T_90 and E_iso distributions using their redshift when it is available, or their pseudo-redshift otherwise. We finally compute the number of GRB (N_Vmax) within the visibility volume (V_max) of each GRB, in order to derive a weight for each detected burst accounting both for the detection significance and the star formation history of the universe. Results: The unbiased distributions obtained clearly show the predominence of X-ray flashes (XRFs) in the global GRB population. We also derive the rate of local GRBs: R0^H2 > 11 Gpc-3 yr-1, which is intermediate between the local rate obtained by considering only the high-luminosity bursts (~1 Gpc-3 yr-1) and that obtained by including the low-luminosity bursts (>200 Gpc-3 yr-1).
