  Closure phases are critical in astronomical interferometry. However, their
uncertainties are difficult to compute numerically. We provide a method to
efficiently compute interferometric closure phase distributions in terms of an
approximate distribution that is valid in the low signal-to-noise ratio regime.
This is done by first showing that the true phase distribution is well
approximated by the von Mises distribution, then performing a convolution of
three von Mises distributions. The resulting approximation is superior than the
normal distribution for all signal-to-noise ratios and, being fully analytic,
allow for fast computations in statistical algorithms.
