The Möbius distribution on the disc |
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Authors: | M C Jones |
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Institution: | (1) Department of Statistics, The Open University, Walton Hall, MK7 6AA Milton Keynes, UK |
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Abstract: | A simple new family of distributions is proposed which has support the unit disc in two dimensions. The density functions
of the family are unimodal, monotonic or uniantimodal. The bivariate symmetric beta distributions, which include the uniform
distribution, are special cases, but many members of the family are skew. The distributions have three parameters, one controlling
orientation, one controlling degree of concentration and the third controlling skewness, or more precisely off-centredness.
Importantly, these parameters are globally orthogonal. An illustrative example of fitting the model to data is given. Conditional
and marginal distributions are considered. The new distributions are compared favourably with an earlier suggestion of the
same author. |
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Keywords: | Beta distribution bivariate distribution circular law M?bius transformation Pearson type II distribution |
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