Abstract
In this paper we discuss the discretization of distributions belonging to some max-domain of attraction. Given a random variable X its discretization is defined as the minimal integer not less than X. Our first interest is on distributions that preserve the max-domain property after discretization. Secondly, we characterize the distributions which are regarded as the discretization of the distribution in the Gumbel max-domain of attraction. Lastly the correspondence of distribution in Gumbel max-domain of attraction is investigated.
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This study was carried out under the ISM Cooperative Research Program (2007-ISM · CRP-5009, 2008-ISM · CRP-5005, 5006).
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Shimura, T. Discretization of distributions in the maximum domain of attraction. Extremes 15, 299–317 (2012). https://doi.org/10.1007/s10687-011-0137-7
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DOI: https://doi.org/10.1007/s10687-011-0137-7