Analytical formulation of the single-visit completeness joint probability density function
Daniel Garrett, Dmitry Savransky
TL;DR
This paper derives an exact analytical formulation for the joint probability density function of single-visit completeness in exoplanet surveys, enabling precise assessment of detection probabilities for various planetary parameters.
Contribution
It introduces a novel analytical method for calculating the joint probability density function of single-visit completeness, extending previous work and improving computational efficiency.
Findings
Exact formulation matches Monte Carlo simulations
Extended the region of nonzero probability values
Demonstrated computational efficiency and accuracy
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 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
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