  Local roughness distributions (LRDs) are studied in the growth regimes of
lattice models in the Kardar-Parisi-Zhang (KPZ) class in 1+1 and 2+1 dimensions
and in a model of the Villain-Lai-Das Sarma (VLDS) growth class in 2+1
dimensions. The squared local roughness w_2 is defined as the variance of the
height inside a box of lateral size r and the LRD P_r(w_2) is sampled as this
box glides along a surface with size L >> r. The variation coefficient C and
the skewness S of the distributions are functions of the scaled box size r /
xi, where xi(t) is a correlation length. For r <~ 0.3 xi, plateaus of C and S
are observed, but with a small time dependence. For a quantitative
characterization of the universal LRD, extrapolation of these values with
power-law corrections in time are performed. The reliability of this procedure
is confirmed in 1+1 dimensions by comparison of results of the restricted
solid-on-solid model and theoretically predicted values of Edwards-Wilkinson
interfaces. For r >> xi, C and S vanish because the LRD converges to a Dirac
delta function. This confirms the inadequacy of extrapolations of amplitude
ratios to r -> infinity, as proposed in recent works. On the other hand, it
highlights the advantage of scaling LRDs by the average instead of scaling by
the variance due to the usually higher accuracy of C compared to S. The scaled
LRD of the VLDS model is very close to the KPZ one due to the small difference
between their variation coefficients and the plateaus of C and S are very
narrow due to the slow time increase of xi. These results suggest that
experimental LRDs obtained in short growth times and with limited resolution
may be inconclusive to determine their universality classes if data accuracy is
low and/or data extrapolation to the long time limit is not feasible.
