  Recently it has been recognized that the so-called generalized Wigner
distribution may provide at least as good a description of terrace width
distributions (TWDs) on vicinal surfaces as the standard Gaussian fit and is
particularly applicable for weak repulsions between steps, where the latter
fails. Subsequent applications to vicinal copper surfaces at various
temperatures confirmed the serviceability of the new analysis procedure but
raised some theoretical questions. Here we address these issues using
analytical, numerical, and statistical methods. We propose an extension of the
generalized Wigner distribution to a two-parameter fit that allows the terrace
widths to be scaled by an optimal effective mean width. We discuss
quantitatively the approach of a Wigner distribution to a Gaussian form for
strong repulsions, how errors in normalization or mean affect the deduced
interaction, and how optimally to extract the interaction from the variance and
mean of the TWD. We show that correlations reduce by two orders of magnitude
the number of {\em independent} measurements in a typical STM image. We also
discuss the effect of the discreteness ("quantization") of terrace widths,
finding that for high misorientation (small mean width) the standard continuum
analysis gives faulty estimates of step interactions.
