We present a mathematical analysis of the statistical parallax method. The method yields physical insight into the maximum-likelihood determinations of the luminosity and velocity distribution and enables us to conduct a vigorous Monte Carlo investigation into various systematic effects. We apply our analytic formalism to the RR Lyrae sample of Layden et al. The velocity distribution of RR Lyrae stars is highly non-Gaussian, with kurtoses K_π= 2.04, K_θ= 3.22 and K_z = 4.28 in the three pri...
