  The variation of a class of Orlicz moments with respect to the Asplund sum
within the class of log-concave functions is demonstrated. Such a variational
formula naturally leads to a family of dual Orlicz curvature measures for
log-concave functions. They are functional analogs of dual (Orlicz) curvature
measures for convex bodies. Partial existence results for the functional dual
Orlicz Minkowski problem are shown.
