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On Joint Estimation of an Exponent of Regular Variation and an Asymmetry Parameter for Tail Distributions

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Sums, Trimmed Sums and Extremes

Part of the book series: Progress in Probability ((PRPR,volume 23))

Abstract

A random variable X is said to have a joint tail distribution which is regularly varying of index -α if for each c > 0,

$$ \mathop {\lim }\limits_{t \to \infty } \frac{{P(\left| X \right| > \,ct)}}{{P(|X|\, > \,t)}}\, = \,c^{ - \alpha }.$$

Supportedx in part by NSF grant DMS-87-02878.

Supported in part by NSF grants DMS-87-02878 and DMS-88-96217.

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References

  • Csorgo, S., P. Deheuvels, and D. M. Mason (1985). Kernel estimates of the tail index of a distribution. Ann. Statist 13, 1050–1077.

    Article  MathSciNet  Google Scholar 

  • Davis, R. and S. I. Resnick (1984). Tail estimates motivated by extreme value theory. Ann. Statist. 12, 1467–1487.

    Article  MathSciNet  MATH  Google Scholar 

  • Feller, W. (1971). An Introduction to Probability Theory and its Applications, Vol. 2. Wiley, New York.

    MATH  Google Scholar 

  • Hahn, M. G., J. Kuelbs, and D. C. Weiner (1990a). The asymptotic joint distribution of self-normalized censored simis and simis-of-squares. Ann. Probab 18, 1284–1341.

    Article  MathSciNet  MATH  Google Scholar 

  • Hahn, M. G., J. Kuelbs, and D. C. Weiner (1990b). Asymptotic behavior of partial sums via trimming and self-normalization. In this volimie.

    Google Scholar 

  • Hall, P. and A. H. Welsh (1984). Best attainable rates of convergence for estimates of parameters of regular variation. Ann. Statist. 12, 1079–1084.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tufts University, Medford, MA, 02155, USA

    Marjorie G. Hahn

  2. Department of Mathematics, Boston University, Boston, MA, 02215, USA

    Daniel C. Weiner

Authors
  1. Marjorie G. Hahn
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  2. Daniel C. Weiner
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Tufts University, 02155, Medford, MA, USA

    Marjorie G. Hahn

  2. Department of Mathematical Sciences, University of Delware, 19716, Newark, DE, USA

    David M. Mason

  3. Department of Mathematics, Boston University, 02215, Boston, MA, USA

    Daniel C. Weiner

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© 1991 Birkhäuser Boston

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Hahn, M.G., Weiner, D.C. (1991). On Joint Estimation of an Exponent of Regular Variation and an Asymmetry Parameter for Tail Distributions. In: Hahn, M.G., Mason, D.M., Weiner, D.C. (eds) Sums, Trimmed Sums and Extremes. Progress in Probability, vol 23. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6793-2_4

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  • DOI: https://doi.org/10.1007/978-1-4684-6793-2_4

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-6795-6

  • Online ISBN: 978-1-4684-6793-2

  • eBook Packages: Springer Book Archive

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