Convergence for the Sample Extremes Via Convolutions

Michel Broniatowski
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Michel Broniatowski: Université Paris 6 4, L.S.T.A.

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 43-52 from Springer

Abstract: Abstract A new proof of Gnedenko’s theorem for the convergence to the Frêchet extreme distributions is presneted. The proof makes use of the theory of stable laws on R+. Uniform rates of convergence are obtained. The paper highlights the role of mixtures of exponential distributions in extreme value theory.

Keywords: Extreme value distributions; rate of convergence; stable laws; mixture of exponentials; Tauberian theorem; Primary 62G30; Secondary 60F05 (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3963-9_5

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DOI: 10.1007/978-94-009-3963-9_5

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