On an extension of the von Mises distribution due to Batschelet

Arthur Pewsey; Kunio Shimizu; Rolando de la Cruz

doi:10.1080/02664761003759024

On an extension of the von Mises distribution due to Batschelet

Arthur Pewsey, Kunio Shimizu, Rolando de la Cruz

Faculty of Engineering and Science

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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 likelihoodbased 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.

Original language	English
Pages (from-to)	1073-1085
Number of pages	13
Journal	Journal of Applied Statistics
Volume	38
Issue number	5
DOIs	https://doi.org/10.1080/02664761003759024
State	Published - May 2011

Keywords

Jones-Pewsey family
Leptokurtic
Likelihood inference
Platykurtic
Symmetric unimodal distributions
Von Mises distribution
Wrapped symmetric stable family
Wrapped t family

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10.1080/02664761003759024

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title = "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 likelihoodbased 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",

author = "Arthur Pewsey and Kunio Shimizu and {de la Cruz}, Rolando",

note = "Funding Information: 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.",

year = "2011",

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doi = "10.1080/02664761003759024",

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AU - Shimizu, Kunio

AU - de la Cruz, Rolando

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AB - 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 likelihoodbased 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.

KW - Jones-Pewsey family

KW - Leptokurtic

KW - Likelihood inference

KW - Platykurtic

KW - Symmetric unimodal distributions

KW - Von Mises distribution

KW - Wrapped symmetric stable family

KW - Wrapped t family

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JO - Journal of Applied Statistics

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On an extension of the von Mises distribution due to Batschelet

Abstract

Keywords

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