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Statistical Distributions in Scientific Work pp 243–254Cite as

Distributions with Sufficient Statistics for Multivariate Location Parameter and Transformation Parameter

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Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 79))

Summary

The form of distributions with sufficient statistics for multivariate location parameter is discussed, and a formula for the rank of such family is obtained. We also give generalizations of these formulas for more general transformation parameters.

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References

  • Dynkin, E. B. (1951). Necessary and sufficient statistics for a family of probability distributions. Uspehi Matematiceskih Nauk., 6, 68–90. English translation in Selected Translations in Mathematical Statistics and Probability, 1, 23–41.

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  • Maksimov, V. M. (1967). Necessary and sufficient statistics for the family of shifts of probability distributions on continuous bicompact groups. Theory of Probability and its Applications (English Translation), 12, 267–280.

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  • Roy, K. K. (1975). Exponential families of densities on an analytic group and sufficient statistics. Sankhya, Series A, 37, 82–92.

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  • Rukhin, A. L. (1975). Characterizations of distributions by statistical properties on groups. In Statistical Distributions in Scientific Work, Vol. III, G. P. Patil, S. Kotz, and J. K. Ord, eds. Reidel, Dordrecht-Holland. Pages 173–184

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  • Rukhin, A. L. (1976). Remark on distributions with sufficient statistics for a multidimensional location parameter. Theory of Probability and Mathematical Statistics, 11, 155–160.

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  • Suprunenko, D. A. and Tyshkevich, R. I. (1968). Commutative Matrices. Academic Press, New York.

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Author information

Authors and Affiliations

  1. Department of Statistics, Purdue University, West Lafayette, Indiana, 47907, USA

    Andrew L. Rukhin

Authors
  1. Andrew L. Rukhin
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Editor information

Editors and Affiliations

  1. Department of Statistics, The Pennsylvania State University, University Park, Pennsylvania, USA

    Charles Taillie  & Ganapati P. Patil  & 

  2. Instituto di Calcolo delle Probabilità, Facoltà di Scienze Statistische Demografiche e Attuariali, Università degli Studi di Roma, Italy

    Bruno A. Baldessari

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© 1981 D. Reidel Publishing Company

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Rukhin, A.L. (1981). Distributions with Sufficient Statistics for Multivariate Location Parameter and Transformation Parameter. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8549-0_20

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  • DOI: https://doi.org/10.1007/978-94-009-8549-0_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-8551-3

  • Online ISBN: 978-94-009-8549-0

  • eBook Packages: Springer Book Archive

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