A Review of Wrapped Distributions for Circular Data

Author:

Bell William1,Nadarajah Saralees1

Affiliation:

1. Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

Abstract

The wrapped method is the most widely used method for constructing distributions for circular data. In this paper, we provide a review of all known wrapped distributions, including 45 distributions for continuous circular data and 10 distributions for discrete circular data. For each wrapped distribution, we state its nth trigonometric moment, mean direction, mean resultant length, skewness, and kurtosis. We also discuss data applications and limitations of each wrapped distribution. This review could be a useful reference and encourage the development of more wrapped distributions. We also mention an R package available for fitting all of the reviewed distributions and illustrate its applications.

Publisher

MDPI AG

Reference67 articles.

1. Fisher, N.I. (1996). Statistical Analysis of Circular Data, Cambridge University Press.

2. Fisher, N.I. (2011). Statistical Analysis of Circular Data, Cambridge University Press.

3. On families of distributions with shape parameters;Jones;Int. Stat. Rev.,2015

4. Ley, C., and Verdebout, T. (2017). Modern Directional Statistics, CRC Press.

5. Recent advances in directional statistics;Pewsey;Test,2021

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