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2 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.

  • The Logarithmic Skew-Normal Distributions are Moment-Indeterminate

  • Part of
  • Gwo Dong Lin, Jordan Stoyanov
  • Journal:
    Journal of Applied Probability / Volume 46 / Issue 3 / September 2009
    Published online by Cambridge University Press:
    14 July 2016, pp. 909-916
    Print publication:
    September 2009
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  • We study the class of logarithmic skew-normal (LSN) distributions. They have heavy tails; however, all their moments of positive integer orders are finite. We are interested in the problem of moments for such distributions. We show that the LSN distributions are all nonunique (moment-indeterminate). Moreover, we explicitly describe Stieltjes classes for some LSN distributions; they are families of infinitely many distributions, which are different but have the same moment sequence as a fixed LSN distribution.