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A Modern Course on Statistical Distributions in Scientific Work pp 213–226Cite as

Weak Convergence for Exponential and Monotone Likelihood Ratio Families and the Convergence of Confidence Limits

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

Summary

Two convergence theorems for one-sided confidence limits for exponential and monotone likelehood ratio families are given. In addition, for some special exponential families, the class of discrete limit distributions is characterized and a uniqueness result obtained. Examples of the above results are given. Applications to hypothesis testing and confidence limits are indicated.

Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462 and das Mathematisches Institut der Technischen Universität München.

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References

  1. Buehler, R. J. (1957). J. Amer. Statist. Assoc. 52, 482–493.

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  2. Harris, B. (1971). J. Amer. Statist. Assoc. 66, 609–617.

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  3. Harris, B. and Soms, A. P. (1974). J. Amer. Statist. Assoc. 69, 259–263.

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  4. Harris, B. and Soms, A. P. (1974). Tables of the two factor and three factor generalized incomplete modified Bessel distributions. In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (eds.). Vol. 3. To appear.

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  5. Hwang, D. (1971). Interval estimation of functions of Bernoulli parameters with reliability and biomedical applications. Technical Report #152, University of Minnesota School of Statistics.

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Author information

Authors and Affiliations

  1. Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, USA

    Bernard Harris

  2. G.D. Searle & Co., Skokie, Illinois, USA

    Andrew P. Soms

Authors
  1. Bernard Harris
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  2. Andrew P. Soms
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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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Harris, B., Soms, A.P. (1975). Weak Convergence for Exponential and Monotone Likelihood Ratio Families and the Convergence of Confidence Limits. 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/10.1007/978-94-010-1842-5_17

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  • DOI: https://doi.org/10.1007/978-94-010-1842-5_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1844-9

  • Online ISBN: 978-94-010-1842-5

  • eBook Packages: Springer Book Archive

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