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

A. S. Praveena () and S. Ravi ()
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A. S. Praveena: University of Mysore
S. Ravi: University of Mysore

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 2, No 18, 1607-1622

Abstract: 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.

Keywords: Exponential normalization; exponential max-domain of attraction; standard log-Fréchet law; subexponential distribution; super-heavy tail; tail equivalence; von-Mises type conditions.; Primary 60G70; Secondary 60E05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13171-022-00304-4

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