  This paper develops methods to study the distribution of Eulerian statistics
defined by second-order recurrence relations. We define a random process to
decompose the statistics over compositions of integers. It is shown that the
numbers of descents in random involutions and in random derangements are
asymptotically normal with a rate of convergence of order $n^{-1/2}$ and
$n^{-1/3}$ respectively.
