A three-parameter generalized von Mises distribution

In this paper, we propose a three-parameter generalized von Mises distribution, called the asymmetric generalized von Mises (AGvM) distribution, which is an extension of the von Mises (vM) distribution, and a subclass of the generalized von Mises (GvM) distribution introduced by Gatto and Jammalamadaka (Stat Methodol 4:341–353, <CitationRef CitationID="CR3">2007</CitationRef>). The three parameter model belongs to an exponential family of distributions and can be used to model both asymmetric and bimodal data. Some properties are studied and interpretation of the parameters is discussed in detail. It is shown that the parameters of the AGvM distribution are particularly easy to interpret and contain a skewness measure as one of its three parameters. A real environmental data set example is provided to illustrate the goodness of fit for AGvM distribution. Copyright Springer-Verlag 2013