Multivariate distributions defined in terms of contours |
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Authors: | Barry C. Arnold,Enrique Castillo,José Marí a Sarabia |
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Affiliation: | 1. Department of Statistics, University of California (Riverside), USA;2. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. Castros, 39005 Santander, Cantabria, Spain;3. Department of Economics, University of Cantabria, Avda. Castros, 39005 Santander, Cantabria, Spain |
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Abstract: | The paper deals with the problem of using contours as the basis for defining probability distributions. First, the most general probability densities with given contours are obtained and the particular cases of circular and elliptical contours are dealt with. It is shown that the so-called elliptically contoured distributions do not include all possible cases. Next, the case of contours defined by polar coordinates is analyzed including its simulation and parameter estimation. Finally, the case of cumulative distribution functions with given contours is discussed. Several examples are used for illustrative purposes. |
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Keywords: | Circular and elliptically contoured distributions Polar coordinates Maximum likelihood |
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