  We calculate an analytical expression for the terrace-width distribution
$P(s)$ for an interacting step system with nearest and next nearest neighbor
interactions. Our model is derived by mapping the step system onto a
statistically equivalent 1D system of classical particles. The validity of the
model is tested with several numerical simulations and experimental results. We
explore the effect of the range of interactions $q$ on the functional form of
the terrace-width distribution and pair correlation functions. For physically
plausible interactions, we find modest changes when next-nearest neighbor
interactions are included and generally negligible changes when more distant
interactions are allowed. We discuss methods for extracting from simulated
experimental data the characteristic scale-setting terms in assumed potential
forms.
