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 here. 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.
Saddlepoint approximations of marginal densities and tail probabilities of general nonlinear statistics are derived. They are based on the expansion of the statistic up to the second order. Their accuracy is shown in a variety of examples, including logit and probit models and rank estimators for regression.
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