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Journal of Probability and Statistics
Volume 2015 (2015), Article ID 165468, 12 pages
Research Article

Convex and Radially Concave Contoured Distributions

Institute of Mathematics, University of Rostock, Ulmenstraße 69, Haus 3, 18057 Rostock, Germany

Received 24 June 2015; Revised 18 October 2015; Accepted 21 October 2015

Academic Editor: Z. D. Bai

Copyright © 2015 Wolf-Dieter Richter. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Integral representations of the locally defined star-generalized surface content measures on star spheres are derived for boundary spheres of balls being convex or radially concave with respect to a fan in . As a result, the general geometric measure representation of star-shaped probability distributions and the general stochastic representation of the corresponding random vectors allow additional specific interpretations in the two mentioned cases. Applications to estimating and testing hypotheses on scaling parameters are presented, and two-dimensional sample clouds are simulated.