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4 results

  • Tail Properties and Asymptotic Expansions for the Maximum of the Logarithmic Skew-Normal Distribution

  • Part of
  • Xin Liao, Zuoxiang Peng, Saralees Nadarajah
  • Journal:
    Journal of Applied Probability / Volume 50 / Issue 3 / September 2013
    Published online by Cambridge University Press:
    30 January 2018, pp. 900-907
    Print publication:
    September 2013
    • Article
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  • We discuss tail behaviors, subexponentiality, and the extreme value distribution of logarithmic skew-normal random variables. With optimal normalized constants, the asymptotic expansion of the distribution of the normalized maximum of logarithmic skew-normal random variables is derived. We show that the convergence rate of the distribution of the normalized maximum to the Gumbel extreme value distribution is proportional to 1/(log n)1/2.

  • Asymptotics of Maxima of Strongly Dependent Gaussian Processes

  • Part of
  • Zhongquan Tan, Enkelejd Hashorva, Zuoxiang Peng
  • Journal:
    Journal of Applied Probability / Volume 49 / Issue 4 / December 2012
    Published online by Cambridge University Press:
    30 January 2018, pp. 1106-1118
    Print publication:
    December 2012
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  • Let {Xn(t), t∈[0,∞)}, n∈ℕ, be standard stationary Gaussian processes. The limit distribution of t∈[0,T(n)]|Xn(t)| is established as rn(t), the correlation function of {Xn(t), t∈[0,∞)}, n∈ℕ, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).

  • Convergence Rate of Extremes for the General Error Distribution

  • Part of
  • Peng Zuoxiang, Saralees Nadarajah, Lin Fuming
  • Journal:
    Journal of Applied Probability / Volume 47 / Issue 3 / September 2010
    Published online by Cambridge University Press:
    14 July 2016, pp. 668-679
    Print publication:
    September 2010
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  • Let {Xn, n ≥ 1} be an independent, identically distributed random sequence with each Xn having the general error distribution. In this paper we derive the exact uniform convergence rate of the distribution of the maximum to its extreme value limit.