Geometric disintegration and star-shaped distributions

• Published in: Journal of statistical distributions and applications Vol. 1; no. 1; p. 1
• Main Author: Richter, Wolf-Dieter
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2014; Springer Nature B.V
• Subjects: 2013 International Conference on Statistical Distributions and Applications; Humanities and Social Sciences; Mathematics and Statistics; multidisciplinary; Science; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Star-generalized von Mises distributions; Star-generalized surface measure; Non-concentric elliptically contoured distributions; Stochastic random vector representation; Intersection-proportion function; p-generalized elliptically contoured distributions; Ball number function; Geometric measure representation; p-generalized ellipsoids and ellipsoidal coordinates; Star-generalized uniform distribution
• ISSN: 2195-5832; 2195-5832
• DOI: 10.1186/s40488-014-0020-6

Geometric and stochastic representations are derived for the big class of p -generalized elliptically contoured distributions, and (generalizing Cavalieri’s and Torricelli’s method of indivisibles in a non-Euclidean sense) a geometric disintegration method is established for deriving even more general star-shaped distributions. Applications to constructing non-concentric elliptically contoured and generalized von Mises distributions are presented. AMS subject classification Primary 60E05; 60D05; secondary 28A50; 28A75; 51F99