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Modelling with star-shaped distributions

Author

Listed:
  • 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)

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.

Suggested Citation

  • Liebscher Eckhard & Richter Wolf-Dieter, 2020. "Modelling with star-shaped distributions," Dependence Modeling, De Gruyter, vol. 8(1), pages 45-69, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:45-69:n:8
    DOI: 10.1515/demo-2020-0003
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    References listed on IDEAS

    as
    1. Wolf-Dieter Richter, 2015. "Convex and Radially Concave Contoured Distributions," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-12, November.
    2. Eckhard Liebscher & Wolf-Dieter Richter, 2016. "Estimation of Star-Shaped Distributions," Risks, MDPI, vol. 4(4), pages 1-37, November.
    3. Batsidis, Apostolos & Zografos, Konstantinos, 2013. "A necessary test of fit of specific elliptical distributions based on an estimator of Song’s measure," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 91-105.
    4. Müller K. & Richter W.-D., 2016. "Extreme value distributions for dependent jointly ln,p-symmetrically distributed random variables," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-33, February.
    5. Wolf-Dieter Richter, 2017. "The Class of ( p , q )-spherical Distributions with an Extension of the Sector and Circle Number Functions," Risks, MDPI, vol. 5(3), pages 1-17, July.
    6. D. Jensen, 1996. "Straight-line models in star-shaped mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 101-117, December.
    7. Wolf-Dieter Richter, 2019. "High-dimensional star-shaped distributions," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-12, December.
    8. Yang, Zhenhai & Kotz, Samuel, 2003. "Center-similar distributions with applications in multivariate analysis," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 335-345, October.
    9. Balkema, A.A. & Embrechts, P. & Nolde, N., 2010. "Meta densities and the shape of their sample clouds," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1738-1754, August.
    10. Eckhard Liebscher, 2016. "Approximation of distributions by using the Anderson Darling statistic," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(22), pages 6732-6745, November.
    11. Hidehiko Kamiya, 2019. "A note on estimation of the shape of density level sets of star-shaped distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(12), pages 3092-3104, June.
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