  We analyze scaling functions in the $3$-$d$, $Z(2)$, $O(2)$ and $O(4)$
universality classes and their finite size dependence using Monte Carlo
simulations of improved $\phi^4$ models. Results for the scaling functions are
fitted to the Widom-Griffiths form, using a parametrization also used in
analytic calculations. We find good agreement on the level of scaling functions
and the location of maxima in the universal part of susceptibilities. We also
find that an earlier parametrization of the $O(4)$ scaling function, using 14
parameters, is well reproduced when using the Widom-Griffiths form with only
three parameters. We furthermore show that finite size corrections to the
scaling functions are distinctively different in the $Z(2)$ and $O(N)$
universality classes and determine the volume dependence of the peak locations
in order parameter and mixed susceptibilities.
