Year: 2023
Type: preprint
Abstract: In this short note, we present a refined approximation for the log-ratio of the density of the von Mises$(μ,κ)$ distribution (also called the circular normal distribution) to the standard (linear) normal distribution when the concentration parameter \k{appa} is large. Our work complements the one of Hill (1976), who obtained a very similar approximation along with quantile couplings, using earlier approximations by Hill & Davis (1968) of Cornish-Fisher type. One motivation for this note is to highlight the connection between the circular and linear normal distributions through their circular variance and (linear) variance.
Source: arXiv (Cornell University)
Author: Ouimet, Frédéric
Institution: McGill University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390438231