Rates of convergence in certain limit theorem for extreme values |
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Authors: | Pavle Mladenovi? Jovan Vukmirovi? |
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Affiliation: | University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Belgrade, Republic of Serbia |
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Abstract: | Let 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 as n→∞, corresponding normalizing constants and the rate of convergence. For an integer r the connection with certain waiting time problems is indicated. |
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Keywords: | Negative binomial distribution Extreme values Rates of convergence Gamma function |
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