  We study the asymptotic behavior of the rank statistic for unimodal
sequences. We use analytic techniques involving asymptotic expansions in order
to prove asymptotic formulas for the moments of the rank. Furthermore, when
appropriately normalized, the values of the unimodal rank asymptotically follow
a logistic distribution. We also prove similar results for Durfee unimodal
sequences and semi-strict unimodal sequences, with the only major difference
being that the (normalized) rank for semistrict unimodal sequences has a
distributional limit of a point mass probability distribution.
