Article: Garrett, D; Savransky, D; “Analytical Formulation of the Single-Visit Completeness Joint Probability Density Function”, Astrophysical Journal, 828(1)
Abstract: We derive an exact formulation of the multivariate integral representing the single-visit obscurational and photometric completeness joint probability density function for arbitrary distributions for planetary parameters. We present a derivation of the region of nonzero values of this function, which extends previous work, and discuss the time and computational complexity costs and benefits of the method. We present a working implementation and demonstrate excellent agreement between this approach and Monte Carlo simulation results.