Convergence properties of Monte Carlo functional expansion tallies

The functional expansion tally (FET) is a method for constructing functional estimates of unknown tally distributions via Monte Carlo simulation. This technique uses a Monte Carlo calculation to estimate expansion coefficients of the tally distribution with respect to a set of orthogonal basis functions. The rate at which the FET approximation converges to the true distribution as the expansion order is increased is developed. For sufficiently smooth distributions the FET is shown to converge faster, and achieve a lower residual error, than a histogram approximation.