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On the Exponential Max-Domain of Attraction of the Standard Log-Fréchet Distribution and Subexponentiality

Author

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  • A. S. Praveena

    (University of Mysore)

  • S. Ravi

    (University of Mysore)

Abstract

In this article, we derive a simple von-Mises type sufficient condition for a distribution function to belong to the exponential max-domain of attraction of the standard log-Fréchet distribution under a nonlinear normalization called exponential normalization. A new criterion for the exponential max-domain, in terms of von-Mises type conditions and tail equivalence, is then derived. Apart from stating some interesting properties of the standard log-Fréchet distribution, some sufficient conditions are obtained for a distribution function to belong to both the exponential max-domain of attraction of the standard log-Fréchet law and the subexponential class. Several examples are discussed.

Suggested Citation

  • A. S. Praveena & S. Ravi, 2023. "On the Exponential Max-Domain of Attraction of the Standard Log-Fréchet Distribution and Subexponentiality," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1607-1622, August.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:2:d:10.1007_s13171-022-00304-4
    DOI: 10.1007/s13171-022-00304-4
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    References listed on IDEAS

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    1. Subramanya, U. R., 1994. "On max domains of attraction of univariate p-max stable laws," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 271-279, March.
    2. S. Ravi & A. S. Praveena, 2015. "On The Intersection Of Max Domains Of Attraction Of p-Max Stable Laws and the Class of Subexponential Distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(1), pages 115-124, January.
    3. Mikosch, Thomas & Resnick, Sidney, 2006. "Activity rates with very heavy tails," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 131-155, February.
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