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1 results

  • The penultimate form of approximation to normal extremes

  • Jonathan P. Cohen
  • Journal:
    Advances in Applied Probability / Volume 14 / Issue 2 / June 1982
    Published online by Cambridge University Press:
    01 July 2016, pp. 324-339
    Print publication:
    June 1982

  • Let Yn denote the largest of n independent N(0,1) random variables. It is shown that the error in approximating the distribution of Yn by the type III extreme value distribution exp {– (–Ax + B)k}, k > 0, is uniformly of order (log n)–2 if and only if the constants A, B and k satisfy certain conditions. In particular, this holds for the penultimate form of Fisher and Tippett (1928). Furthermore, two sufficient conditions are given so that these results can be extended to a stationary Gaussian sequence.