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Journal of Probability and Statistics
Volume 2015, Article ID 165468, 12 pages
http://dx.doi.org/10.1155/2015/165468
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.

Linked References

  1. K.-T. Fang and Y. Zhang, Generalized Multivariate Analysis, Springer, Berlin, Germany, 1990.
  2. T. W. Anderson and K.-T. Fang, “Theory and applications of elliptically contoured and related distributions,” Technical Report 24, Department of Statistics, Stanford University, Stanford, Calif, USA, 1990. View at Google Scholar
  3. M. Bilodeau and D. Brenner, Theory of Multivariate Statistics, Springer, New York, NY, USA, 1999. View at MathSciNet
  4. E. Liebscher, “A semiparametric density estimator based on elliptical distributions,” Journal of Multivariate Analysis, vol. 92, no. 1, pp. 205–225, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. N. Balakrishnan and C.-D. Lai, Continuous Bivariate Distributions, Springer, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. W.-D. Richter, “Geometric disintegration and star-shaped distributions,” Journal of Statistical Distributions and Applications, vol. 1, article 20, 2014. View at Publisher · View at Google Scholar
  7. M. Rudemo and H. Stryhn, “Boundary estimation for star-shaped objects,” in Change-Point Problems, E. Carlstein, H.-G. Müller, and D. Siegmund, Eds., pp. 276–283, Institute of Mathematical Statistics, Hayward, Calif, USA, 1994. View at Google Scholar
  8. A. B. Tsybakov, “On nonparametric estimation of density level sets,” The Annals of Statistics, vol. 25, no. 3, pp. 948–969, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. G. Walther, “Granulometric smoothing,” The Annals of Statistics, vol. 25, no. 6, pp. 2273–2299, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. Cuevas, M. Febrero, and R. Fraiman, “Estimating the number of clusters,” Canadian Journal of Statistics, vol. 28, no. 2, pp. 367–382, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. M. Moszyńska and W.-D. Richter, “Reverse triangle inequality. Antinorms and semi-antinorms,” Studia Scientiarum Mathematicarum Hungarica, vol. 49, no. 1, pp. 120–138, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. W.-D. Richter, “Generalized spherical and simplicial coordinates,” Journal of Mathematical Analysis and Applications, vol. 336, no. 2, pp. 1187–1202, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. W.-D. Richter, “Continuous ln,p-symmetric distributions,” Lithuanian Mathematical Journal, vol. 49, no. 1, pp. 93–108, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. D. M. Levine, T. C. Krehbiel, and M. L. Berenson, Business Statistics: A First Course, Prentice-Hall, 2000.
  15. A. M. Mineo and M. Ruggieri, “A software tool for the exponential power distribution: the normal package,” Journal of Statistical Software, vol. 12, no. 4, pp. 1–24, 2005. View at Google Scholar · View at Scopus
  16. C. Ittrich, D. Krause, and W.-D. Richter, “Probabilities and large quantiles of noncentral generalized chi-square distributions,” Statistics, vol. 34, no. 1, pp. 53–101, 2000. View at Publisher · View at Google Scholar · View at Scopus
  17. S. Kalke and W.-D. Richter, “Simulation of the p-generalized Gaussian distribution,” Journal of Statistical Computation and Simulation, vol. 83, no. 4, pp. 639–665, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. S. Kalke, “pgnorm,” The R Project for Statistical Computing, https://www.r-project.org.