  As a motivating problem, we aim to study some special aspects of the marginal
distributions of the order statistics for exchangeable and (more generally) for
minimally stable non-negative random variables $T_{1},...,T_{r}$. In any case,
we assume that $T_{1},...,T_{r}$ are identically distributed, with a common
survival function $\overline{G}$ and their survival copula is denoted by $K$.
The diagonal's and subdiagonals' sections of $K$, along with $\overline{G}$,
are possible tools to describe the information needed to recover the laws of
order statistics.
  When attention is restricted to the absolutely continuous case, such a joint
distribution can be described in terms of the associated multivariate
conditional hazard rate (m.c.h.r.) functions. We then study the distributions
of the order statistics of $T_{1},...,T_{r}$ also in terms of the system of the
m.c.h.r. functions. We compare and, in a sense, we combine the two different
approaches in order to obtain different detailed formulas and to analyze some
probabilistic aspects for the distributions of interest. This study also leads
us to compare the two cases of exchangeable and minimally stable variables both
in terms of copulas and of m.c.h.r. functions. The paper concludes with the
analysis of two remarkable special cases of stochastic dependence, namely
Archimedean copulas and load sharing models. This analysis will allow us to
provide some illustrative examples, and some discussion about peculiar aspects
of our results.
