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Modelling with star-shaped distributions

Liebscher Eckhard () and Richter Wolf-Dieter ()
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Liebscher Eckhard: University of Applied Sciences Merseburg, Department of Engineering and Natural Sciences, 06217Merseburg, Germany
Richter Wolf-Dieter: University of Rostock, Institute of Mathematics, Ulmenstr. 69, Haus 3, 18057 Rostock, Germany

Dependence Modeling, 2020, vol. 8, issue 1, 45-69

Abstract: We prove and describe in great detail a general method for constructing a wide range of multivariate probability density functions. We introduce probabilistic models for a large variety of clouds of multivariate data points. In the present paper, the focus is on star-shaped distributions of an arbitrary dimension, where in case of spherical distributions dependence is modeled by a non-Gaussian density generating function.

Keywords: convex data cloud; radially concave data cloud; star contoured data cloud; data cloud oriented model; norm sphere; antinorm sphere; star sphere; global shape approximation; locally refined shape approximation; direction dependent model refinement; star-shaped density; estimation; moments; simulation; star generalized trigonometric functions; star generalized coordinates; multivariate p-generalized ellipsoidal coordinates; 60E05; 62E17 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/demo-2020-0003

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