A Review of Wrapped Distributions for Circular Data

William Bell and Saralees Nadarajah ()
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William Bell: Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
Saralees Nadarajah: Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

Mathematics, 2024, vol. 12, issue 16, 1-51

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 n th 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.

Keywords: kurtosis; mean direction; mean resultant length; skewness; trigonometric moment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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