Transmuted distributions and random extrema

Tomasz J. Kozubowski and Krzysztof Podgórski

Statistics & Probability Letters, 2016, vol. 116, issue C, 6-8

Abstract: 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 of independent and identically distributed variables with the base distribution, where 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.

Keywords: Distribution theory; Extremes; Marshall–Olkin generalized distribution; Quadratic transmutation map; Random extrema; Stochastic representation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2016.04.001

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