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A Characterization Theorem Based on Truncated Moments and its Application to Some Distribution Families

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Mathematical Statistics and Probability Theory

Abstract

A new representation theorem for distributions of real-valued random variables is presented. The theorem is based on a relationship between different truncated moments of the same random variable. As an example of its application, characterization theorems for some families of both continuous and discrete distributions are derived. Further applications can be obtained after certain transformations. These characterizations may also serve as a basis for parameter estimation.

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References

  • Glänzel, W., Telcs, A., Schubert, A.: Characterization by Truncated Moments and Its Application to Pearson-type Distributions. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 66 (1984) 173–183.

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  • Glänzel, W.: A Characterization of the Normal Distribution. Studie Sci. Math. Hungarica (to be published in 1987 ).

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  • Glänzel, W.: A Characterization Theorem for Pearson-Type Distributions. (Submitted to Sankhyā Ser. A.).

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  • Schubert, A., Glänzel, W., Mérő, A.: Classification and Identification of Frequency Distributions Using a Characterization Theorem. In: Svab, J., Győrffy, M., Abranyi, A., Kovacs, G. (Eds.), Proc. of the First European Biometric Conference of the Biometric Society, held in Budapest, on April 1–3, 1985.

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Author information

Authors and Affiliations

  1. Information Science and Scientometrics Research Unit, Library of the Hungarian Academy of Sciences, H-1361, Budapest, P.O.Box 7, Hungary

    Wolfgang Glänzel

Authors
  1. Wolfgang Glänzel
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Editor information

Editors and Affiliations

  1. University of Cologne, Germany

    P. Bauer

  2. University of Agriculture, Vienna, Austria

    F. Konecny

  3. Technical University, Vienna, Austria

    W. Wertz

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© 1987 D. Reidel Publishing Company

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Glänzel, W. (1987). A Characterization Theorem Based on Truncated Moments and its Application to Some Distribution Families. In: Bauer, P., Konecny, F., Wertz, W. (eds) Mathematical Statistics and Probability Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3965-3_8

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  • DOI: https://doi.org/10.1007/978-94-009-3965-3_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8259-4

  • Online ISBN: 978-94-009-3965-3

  • eBook Packages: Springer Book Archive

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