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

TL;DR

This paper presents efficient methods for evaluating the probability density function of the wrapped normal distribution by analyzing two truncated series representations, enabling accurate computation with few terms across different uncertainty levels.

Contribution

It introduces and compares two truncated series methods for the wrapped normal distribution, optimizing evaluation accuracy for small and large uncertainties.

Findings

Both series representations achieve high accuracy with few summands.

One method is optimal for small uncertainties, the other for large uncertainties.

Efficient evaluation reduces computational complexity for practical applications.

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.