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Statistical Problems of Size and Shape. II. Characterizations of the Lognormal, Gamma and Dirichlet Distributions

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A Modern Course on Statistical Distributions in Scientific Work

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

Summary

The lognormal distribution is characterized using the concepts of “multiplicative” isometry and neutrality, based on the regular sequence of size variables II s1 X 11/s , s = 1. …,k. There are corresponding characterizations of the Gamma and Dirichlet distributions, using “additive” isometry and neutrality, based on ∑ s1 Xi, s = 1,…k. While the lognormal model is “rich”, still, no member of the lognormal family can exhibit additive isometry or neutrality.

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Author information

Authors and Affiliations

  1. National Institutes of Health, Bethesda, Maryland, USA

    James E. Mosimann

Authors
  1. James E. Mosimann
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Editor information

Editors and Affiliations

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

    G. P. Patil

  2. Temple University, Philadelphia, Pa., USA

    S. 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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Mosimann, J.E. (1975). Statistical Problems of Size and Shape. II. Characterizations of the Lognormal, Gamma and Dirichlet Distributions. 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/10.1007/978-94-010-1845-6_17

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  • DOI: https://doi.org/10.1007/978-94-010-1845-6_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1847-0

  • Online ISBN: 978-94-010-1845-6

  • eBook Packages: Springer Book Archive

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