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Characterizations of Distributions by Statistical Properties on Groups

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Book cover A Modern Course on Statistical Distributions in Scientific Work

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 17))

Summary

The article investigates some characterization problems occurring in mathematical statistics when the sample space is a homogeneous space and a transformation parameter distribution family is considered. We give general form of positive and continuous probability density admitting nontrivial sufficient statistics for this parameter. Conditions of optimality of an equivariant estimators are obtained and some corresponding characterization theorems are stated. We show also that under mild restrictions the transformation parameter family is characterized by distributions of invariant statistics.

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References

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Author information

Authors and Affiliations

  1. Mathematical Institute, Leningrad, U.S.S.R.

    A. L. Rukhin

Authors
  1. A. L. Rukhin
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Editor information

Editors and Affiliations

  1. The Pennsylvania State University, University Park, Pa., USA

    Ganapati P. Patil

  2. Temple University, Philadelphia, Pa., USA

    Samuel Kotz

  3. University of Warwick, Coventry, England

    J. K. Ord

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© 1975 D. Reidel Publishing Company, Dordrecht-Holland

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Rukhin, A.L. (1975). Characterizations of Distributions by Statistical Properties on Groups. In: Patil, G.P., Kotz, S., Ord, J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1848-7_13

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  • DOI: https://doi.org/10.1007/978-94-010-1848-7_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1850-0

  • Online ISBN: 978-94-010-1848-7

  • eBook Packages: Springer Book Archive

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