  We apply the Stein-Chen method to problems from extreme value theory. On the
one hand, the Stein-Chen method for Poisson approximation allows us to obtain
bounds on the Kolmogorov distance between the law of the maximum of i.i.d.
random variables, following certain well known distributions, and an extreme
value distribution. On the other hand, we introduce marked point processes of
exceedances (MPPE's) whose i.i.d. marks can be either univariate or
multivariate. We use the Stein-Chen method for Poisson process approximation to
determine bounds on the error of the approximation, in some appropriate
probability metric, of the law of the MPPE by that of a Poisson process. The
Poisson process that we approximate by has intensity measure equal to that of
the MPPE. In some cases, this intensity measure is difficult to work with, or
varies with the sample size; we then approximate by a further easier-to-use
Poisson process and estimate the error of this additional approximation.
