The generalized von Mises distribution. (English) Zbl 1248.62012

Gatto, Riccardo; Jammalamadaka, Sreenivasa Rao

Stat. Methodol. 4, No. 3, 341-353 (2007).

Summary: A generalization of the von Mises distribution, which is broad enough to cover unimodality as well as multimodality, symmetry as well as asymmetry of circular data, is discussed. We study this distribution in some detail and discuss its many features, some inferential and computational aspects, and provide some important results including characterization properties for this distribution.

MSC:

62E10	Characterization and structure theory of statistical distributions
62F10	Point estimation
62H11	Directional data; spatial statistics
65C60	Computational problems in statistics (MSC2010)

Keywords:

circular distribution; entropy; exponential family; Fourier expansion; maximum likelihood; normal distribution; offset distribution; symmetry; asymmetry; trigonometric moments; unimodality; ultimodality

Software:

circular; CircStats

References:

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