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Geometric Generalization of the Exponential Law

Author

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  • Henschel, V.
  • Richter, W. -D.

Abstract

For the multivariate l1-norm symmetric distributions, which are generalizations of the n-dimensional exponential distribution with independent marginals, a geometric representation formula is given, together with some of its basic properties. This formula can especially be applied to a new developed and statistically well motivated system of sets. From that the distribution of a t-statistic adapted for the two-parameter exponential distribution and its generalizations is determined. Asymptotic normality of this adapted t-statistic is shown under certain conditions.

Suggested Citation

  • Henschel, V. & Richter, W. -D., 2002. "Geometric Generalization of the Exponential Law," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 189-204, May.
    • Handle: RePEc:eee:jmvana:v:81:y:2002:i:2:p:189-204
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    Citations

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    Cited by:

    1. 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.
    2. Wolf-Dieter Richter & Kay Schicker, 2017. "Simulation of polyhedral convex contoured distributions," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-19, December.
    3. Wolf-Dieter Richter, 2019. "High-dimensional star-shaped distributions," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-12, December.
    4. Volkmar Henschel, 2002. "Statistical inference in simplicially contoured sample distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 56(3), pages 215-228, December.

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