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Statistical inference in simplicially contoured sample distributions

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Abstract

For generalizations of the n-dimensional two parameter exponential distribution with identical marginals with threshold and dispersion parameters the exact distributions of estimators and test statistics are given. Under cer-tain conditions the consistency of the estimators and the rate of convergence is shown. Therefore generalized Gamma- and F-distributions are defined.

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References

  1. Fan J (1984) Generalized non-central t-, f - and T2-distributions. Journal of Graduate School, 134–148

  2. Fang B-Q, Fang K-T (1988) Some families of multivariate symmetric distributions related to exponential distributions. Journal of Multivariate Analysis 24:109–122

    Article  MATH  MathSciNet  Google Scholar 

  3. Fang B-Q, Fang K-T (1988) MLE and LRC for location and scale parameters of the l1-norm symmetric multivariate distribution. Acta Math. Appl. Sinica (English Series) 4:13–22

    Article  MATH  Google Scholar 

  4. Fang B-Q, Fang K-T (1988) Distribution of order statistics of the l1-norm symmetric multi-variate distributions and application. Chinese J. Appl. Prob. Statist. 4:46–54

    Google Scholar 

  5. Fang K-T, Anderson TW editors (1990) Statistical inference in elliptically contoured and re-ated distributions. NY: Allerton Press Inc., New York

  6. Fang K-T, Kotz S, Ng KW (1990) Symmetric multivariate and related distributions. Chapman and Hall, London, New York

    Book  MATH  Google Scholar 

  7. Gupta RD, Richards DStP (1987) Multivariate liouville distributions. Journal of Multivariate Analysis 23:233–256

    Article  MATH  MathSciNet  Google Scholar 

  8. Henschel V, Richter W-D (2002) Geometric generalization of the exponential law. Journal of Multivariate Analysis, to appear

  9. Kelker D (1970) Distribution theory of spherical distributions and location scale parameter generalization. Sankhyā A:419–430

    MathSciNet  Google Scholar 

  10. Rényi A (1973) Wahrscheinlichkeitsrechnung. VEB Deutscher Verlag der Wissenschaften, Berlin

    Google Scholar 

  11. Richter W-D (1991) Eine geometrische Methode in der Stochastik. Rostocker Mathematisches Kolloquium 44:63–72

    MATH  Google Scholar 

  12. Sukhatme PV (1937) The test of significance for samples of the χ2-population with two degrees of freedom. Annales of Eugenics 8:52–66

    Article  Google Scholar 

  13. Witting H, Müller-Funk U (1995) Mathematische Statistik II. Asymptotische Statistik: Para-metrische Modelle und nichtparametrische Funktionale. B.G. Teubner, Stuttgart

    Google Scholar 

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Correspondence to Volkmar Henschel.

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Henschel, V. Statistical inference in simplicially contoured sample distributions. Metrika 56, 215–228 (2002). https://doi.org/10.1007/s001840100174

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