Transmuted distributions and random extrema

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• 作者：Tomasz J. Kozubowski^a ; ^{tkozubow@unr.edu" class="auth_mail" title="E-mail the corresponding author} ; Krzysztof Podgó ; rski^b
• 关键词：Distribution theory ; Extremes ; Marshall&ndash ; Olkin generalized distribution ; Quadratic transmutation map ; Random extrema ; Stochastic representation
• 刊名：Statistics & Probability Letters
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：116
• 期：Complete
• 页码：6-8
• 全文大小：319 K

文摘

Recent years have seen an increased interest in the transmuted probability models, which arise from transforming a “base” distribution into its generalized counterpart. While many standard probability distributions were generalized throughout this construction, the concept lacked deeper theoretical interpretation. We show that the transmuted distributions can be viewed as the distribution of maxima (or minima) of a random number N$N$ of independent and identically distributed variables with the base distribution, where N$N$ has a Bernoulli distribution shifted up by one. Consequently, the transmuted models are a special case of extremal distributions defined through a more general N$N$.