The angular distribution of the diffracted intensity from a crystal surface in a reflection electron diffraction experiment is sensitive to the defect structure of the surface. For a surface with atomic steps, the diffracted beams can be split or broadened with the shape determined by the distribution of steps. For a surface with a finite number of levels we have previously shown that in general the angular profile across a diffracted beam is the sum of a central spike, due to the long range ofder of the surface, plus one or more broad functions, due to the step disorder. The explicit shapes of the broad functions were previously calculated for a one-dimensional geometric model of the disorder that corresponded to the limiting case of non-interacting steps. In this paper, we extend the calculation to treat any one-dimensional distribution of steps which does not depend upon choice of origin and for which the surface consists of either (1) an infinite number of levels, each with identical terrace length distributions or (2) a finite number of levels, but with different distributions allowed. The results of the calculation are compared to reflection high-energy electron diffraction (RHEED) measurements from vicinal and singular GaAs(001) surfaces prepared by molecular beam epitaxy (MBE). For the vicinal surfaces, the staircase step distribution is observed to order on crossing a surface phase transition. The measured profiles agree with a calculation that assumes a minimum terrace length. For the singular surface, steps are observed to appear after the same transition is crossed. These latter profiles cannot be described by a one-dimensional geometric step distribution. The behavior of these two systems are discussed in terms of the increased evaporation rate at temperature above this phase transition.