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Convex and Radially Concave Contoured Distributions

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  • Wolf-Dieter Richter

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 . 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.

Suggested Citation

  • Wolf-Dieter Richter, 2015. "Convex and Radially Concave Contoured Distributions," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-12, November.
    • Handle: RePEc:hin:jnljps:165468
    DOI: 10.1155/2015/165468
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    Cited by:

    1. Liebscher Eckhard & Richter Wolf-Dieter, 2020. "Modelling with star-shaped distributions," Dependence Modeling, De Gruyter, vol. 8(1), pages 45-69, January.
    2. Liebscher Eckhard & Richter Wolf-Dieter, 2020. "Modelling with star-shaped distributions," Dependence Modeling, De Gruyter, vol. 8(1), pages 45-69, January.
    3. Müller K. & Richter W.-D., 2017. "Exact distributions of order statistics from ln,p-symmetric sample distributions," Dependence Modeling, De Gruyter, vol. 5(1), pages 221-245, August.
    4. Wolf-Dieter Richter, 2019. "On Ball Numbers," Mathematics, MDPI, vol. 7(8), pages 1-10, August.

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