  In this paper, we study the degenerate derangement polynomials and numbers,
investigate some properties of those polynomials and numbers and explore their
connections with the degenerate gamma distributions. In more detail, we derive
their explicit expressions, recurrence relations and some identities involving
the degenerate derangement polynomials and numbers and other special
polynomials and numbers, which include the fully degenerate Bell polynomials,
the degenerate Fubini polynomials and the degenerate Stirling numbers of both
kinds. We also show that those polynomials and numbers are connected with the
moments of some variants of the degenerate gamma distributions.
