Tail properties and asymptotic expansions for the maximum of the logarithmic skew-normal distribution.

• Autores: Xin Liao, Zuoxiang Peng, Saralees Nadarajah
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 50, Nº. 3, 2013, págs. 900-907
• Idioma: inglés
• DOI: 10.1239/jap/1378401246
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• Resumen

  • 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)½.