  Stirling permutations are parking functions, and we investigate two parking
function statistics in the context of these objects: lucky cars and
displacement. Among our results, we consider two extreme cases: extremely lucky
Stirling permutations (those with maximally many lucky cars) and extremely
unlucky Stirling permutations (those with exactly one lucky car). We show that
the number of extremely lucky Stirling permutations of order $n$ is the Catalan
number $C_n$, and the number of extremely unlucky Stirling permutations is
$(n-1)!$. We also give some results for luck that lies between these two
extremes. Further, we establish that the displacement of any Stirling
permutation of order $n$ is $n^2$, and we prove several results about
displacement composition vectors. We conclude with directions for further
study.
