Rates of convergence in certain limit theorem for extreme values

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:363

Article

Mladenovic, Pavle¹  Vukmirovic, Jovan¹ 

[1] Univ Belgrade, Fac Math, Belgrade 11000, Serbia

关键词: Negative binomial distribution;    Extreme values;    Rates of convergence;    Gamma function;   

DOI  :  10.1016/j.jmaa.2009.08.044

来源: Elsevier

【 摘 要 】

Let X(n1)*, ..., X(nn)* be independent random variables with the common negative binomial distribution with parameters r > 0 and 1/n, where r is not necessarily an integer. We determine the limiting distribution of the random variable M(n)* = max{X(n1)*, ..., X(nn)*} as n -> infinity, corresponding normalizing constants and the rate of convergence. For an integer r the connection with certain waiting time problems is indicated. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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