  A sample of 427 gamma-ray bursts from a database (February 2002 - April 2008)
of the RHESSI satellite is analyzed statistically. The spectral lags and
peak-count rates, which have been calculated for the first time in this paper,
are studied completing an earlier analysis of durations and hardness ratios.
The analysis of the RHESSI database has already inferred the existence of a
third group with intermediate duration, apart from the so-called short and long
groups. First aim of this article is to discuss the properties of these
intermediate-duration bursts in terms of peak-count rates and spectral lags.
Second aim is to discuss the number of GRB groups using another statistical
method and by employing the peak-count rates and spectral lags as well. The
standard parametric (model-based clustering) and non-parametric (K-means
clustering) statistical tests together with the Kolmogorov-Smirnov and
Anderson-Darling tests are used. Two new results are obtained: A. The
intermediate-duration group has similar properties to the group of short
bursts. Intermediate and long groups appear to be different. B. The
intermediate-duration GRBs in the RHESSI and Swift databases seem to be
represented by different phenomena.
