On parameter orthogonality in symmetric and skew models |
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Authors: | MC Jones Karim Anaya-Izquierdo |
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Institution: | Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK |
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Abstract: | Orthogonal and partly orthogonal reparametrisations are provided for certain wide and important families of univariate continuous distributions. First, the orthogonality of parameters in location-scale symmetric families is extended to symmetric distributions involving a third parameter. This sets the scene for consideration of the four-parameter situation in which skewness is also allowed. It turns out that one specific approach to generating such four-parameter families, that of two-piece distributions with a certain parametrisation restriction, has some attractive features with regard to parameter orthogonality which, to the best of our knowledge, are not shared with other four-parameter distributions. Our work also affords partly orthogonal parametrisations of three-parameter two-piece models. |
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Keywords: | Extended location-scale model Skew-t distribution Two-piece distribution |
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