Efficient Evaluation of the Probability Density Function of a Wrapped Normal Distribution

Abstract

The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an infinite series is involved. In this paper, we investigate the evaluation of two truncated series representations. As one representation performs well for small uncertainties whereas the other performs well for large uncertainties, we show that in all cases a small number of summands is sufficient to achieve high accuracy.