Extreme values are considered in samples with random size that have a mixed Poisson distribution generated by a doubly stochastic Poisson process. Limit theorems are proved for the distributions of max-compound Cox processes establishing necessary and sufficient conditions for the convergence of these distributions.
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Proceedings of the XXXV International Seminar on Stability Problems for Stochastic Models, Perm, Russia, September 24–28, 2018. Part I.
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Korolev, V., Sokolov, I. & Gorshenin, A. Max-Compound Cox Processes. II. J Math Sci 246, 488–502 (2020). https://doi.org/10.1007/s10958-020-04754-9
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DOI: https://doi.org/10.1007/s10958-020-04754-9