  In this paper, the $q$-th dual curvature measure is extended to convex
functions and the associated Minkowski problem is posed. A special case
includes the $q$-th dual curvature measure of convex bodies which defined by
Huang, Lutwak, Yang and Zhang. Existence for the functional dual Minkowski
problem is showed when $q\leq0$ and the uniqueness part is obtained with some
assumptions.
