Convex and Radially Concave Contoured Distributions. (23rd November 2015)

• Record Type: Journal Article
• Authors: Richter, Wolf-Dieter
• Other Names: Bai Z. D. Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2015(2015)
• Publication Date: 2015-11-23
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2015/165468
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : 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 R n . 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.