On an extension of the von Mises distribution due to Batschelet

Abstract

This paper considers the three-parameter family of symmetric unimodal circular distributions proposed by Batschelet in [1], an extension of the von Mises distribution containing distributional forms ranging from the highly leptokurtic to the very platykurtic. The family's fundamental properties are given, and likelihood-based techniques described which can be used to perform estimation and hypothesis testing. Analyses are presented of two data sets which illustrate how the family and three of its most direct competitors can be applied in the search for parsimonious models for circular data.

Keywords:

• Jones–Pewsey family
• leptokurtic
• likelihood inference
• platykurtic
• symmetric unimodal distributions
• von Mises distribution
• wrapped symmetric stable family
• wrapped t family

Acknowledgements

The authors thank Dr Ian Evans for kindly letting them have access to the glacial cirque data. Dr Pewsey expresses his most sincere gratitude to the Department of Mathematics at Keio University for its warm hospitality and COE funding during the research visit which led to the production of this paper. His research was also partially funded by project MTM2007-61470 of the Spanish Ministry of Education and Science. Dr Cruz was supported by FONDECYT grant 11080017.