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Transmuted distributions and random extrema

Author

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  • Kozubowski, Tomasz J.
  • Podgórski, Krzysztof

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.

Suggested Citation

  • Kozubowski, Tomasz J. & Podgórski, Krzysztof, 2016. "Transmuted distributions and random extrema," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 6-8.
    • Handle: RePEc:eee:stapro:v:116:y:2016:i:c:p:6-8
    DOI: 10.1016/j.spl.2016.04.001
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    References listed on IDEAS

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    1. Daniele Cristina Tita Granzotto & Francisco Louzada, 2015. "The Transmuted Log-Logistic Distribution: Modeling, Inference, and an Application to a Polled Tabapua Race Time up to First Calving Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(16), pages 3387-3402, August.
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    Cited by:

    1. Tomasz J. Kozubowski & Krzysztof Podgórski, 2018. "Kumaraswamy Distribution and Random Extrema," The Open Statistics and Probability Journal, Bentham Open, vol. 9(1), pages 18-25, July.

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