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Abstract <p>As the well known extreme value law, the Fréchet law, is the standard example of ‘‘heavy tail,’’ the log-Fréchet and the log-log-Fréchet laws are standard examples of ‘‘super heavy tails.’’ New characterizations of max-domains of attraction of standard log-Fréchet and log-log-Fréchet laws, based on integral representations, are obtained in this article. Several illustrations are discussed including an example involving the Tracy-Widom distribution.</p>

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On Standard Log-Fréchet and Log-log-Fréchet Laws

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • A. S. Praveena,
  • S. Ravi

摘要

Abstract

As the well known extreme value law, the Fréchet law, is the standard example of ‘‘heavy tail,’’ the log-Fréchet and the log-log-Fréchet laws are standard examples of ‘‘super heavy tails.’’ New characterizations of max-domains of attraction of standard log-Fréchet and log-log-Fréchet laws, based on integral representations, are obtained in this article. Several illustrations are discussed including an example involving the Tracy-Widom distribution.