  We define and study positional marked patterns. A positional marked pattern
is a permutation $\tau$ where one of elements in $\tau$ is underlined. Given a
permutation $\sigma$, we say that $\sigma$ is $\tau$-match at position $i$ if
$\tau$ occurs in $\sigma$ in such a way that $\sigma_i$ plays the role of the
underlined element in the occurrence. We let $pmp_\tau(\sigma)$ denote the
number of position $i$ which $\sigma$ is $\tau$-match. This defines a new class
of statistics on permutations, where we study such statistics and prove a
number of results. In particular, we prove that two positional marked patterns
$1\underline{2}3$ and $1\underline{3}2$ give rise to two statistics that have
the same distribution. The equidistibution phenomenon also occurs in other
several pairs of patterns like $1\underline{2}3$ and $1\underline{3}2$, which
we prove in this dissertation.
