  The notion of stochastic precedence between two random variables emerges as a
relevant concept in several fields of applied probability. When one consider a
vector of random variables $X_1,...,X_n$, this notion has a preeminent role in
the analysis of minima of the type $\min_{j \in A} X_j$ for $A \subset \{1,
\ldots n\}$. In such an analysis, however, several apparently controversial
aspects can arise (among which phenomena of "non-transitivity").
  Here we concentrate attention on vectors of non-negative random variables
with absolutely continuous joint distributions, in which a case the set of the
multivariate conditional hazard rate (m.c.h.r.) functions can be employed as a
convenient method to describe different aspects of stochastic dependence.
  In terms of the m.c.h.r. functions, we first obtain convenient formulas for
the probability distributions of the variables $\min_{j \in A} X_j$ and for the
probability of events $\{X_i=\min_{j \in A} X_j\}$. Then we detail several
aspects of the notion of stochastic precedence. On these bases, we explain some
controversial behavior of such variables and give sufficient conditions under
which paradoxical aspects can be excluded. On the purpose of stimulating active
interest of readers, we present several comments and pertinent examples.
