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

  • Marjorie G. Hahn
  • Daniel C. Weiner
Part of the Progress in Probability book series (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,
$$ \mathop {\lim }\limits_{t \to \infty } \frac{{P(\left| X \right| > \,ct)}}{{P(|X|\, > \,t)}}\, = \,c^{ - \alpha }.$$

Keywords

Asymptotic Normality Optimal Rate Asymmetry Parameter Regular Variation Bias Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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

Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • Marjorie G. Hahn
    • 1
  • Daniel C. Weiner
    • 2
  1. 1.Department of MathematicsTufts UniversityMedfordUSA
  2. 2.Department of MathematicsBoston UniversityBostonUSA

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