Convergence rates of limit distribution of maxima of lognormal samples

Let Mn denote the partial maximum of an independent and identically distributed lognormal random sequence. In this paper, we derive the exact uniform convergence rate of the distribution of the normalized maximum (Mn−bn)/an to its extreme value distribution, where the constants an and bn are chosen...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2012-11, Vol.395 (2), p.643-653
Main Authors: Liao, Xin, Peng, Zuoxiang
Format: Article
Language:English
Subjects:
Extreme value distribution
Logarithmic normal distribution
Maximum
Uniform convergence rate
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Summary:Let Mn denote the partial maximum of an independent and identically distributed lognormal random sequence. In this paper, we derive the exact uniform convergence rate of the distribution of the normalized maximum (Mn−bn)/an to its extreme value distribution, where the constants an and bn are chosen by an optimal way.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.05.077