  The two widely accepted classes of gamma-ray bursts (GRBs), short and long,
are with confidence ascribed to mergers of compact objects and collapse of
massive stars, respectively. A third, intermediate/soft class, remains
putative. Its existence was claimed based on univariate and bivariate analyses
of GRB observables modeled with Gaussian distributions. This, however, may not
be the appropriate approach, as it has been already shown that the univariate
distributions of durations are better described by mixtures of two skewed
components rather than three Gaussian ones.
  This paper investigates whether data in the duration--hardness ratio plane is
better modeled by mixtures of skewed bivariate distributions than by normal
ones. The archival data set of the Compton Gamma-Ray Observatory/BATSE and
Fermi/GBM data from the most recent catalogue release are examined. The
preferred model is chosen based on two information criteria, Akaike ($AIC$) and
Bayesian ($BIC$). It is found that the best description is given by a
two-component mixture of skewed Student-$t$ distributions, which outperforms
any other model considered. This implies that the distribution of the studied
parameters is intrinsically skewed, introducing spurious Gaussian components,
and hence the third class is unlikely to be a real phenomenon. Its existence,
based on statistical inference, is therefore rejected as unnecessary to explain
the observations.
