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Multiple q -Integral and Records from Geometrically Distributed Sequences

Author

Listed:
  • Fernando López-Blázquez

    (Departamento de Estadística e I.O., Universidad de Sevilla, 41012 Seville, Spain
    Current address: Facultad de Matemáticas, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain.
    These authors contributed equally to this work.)

  • Begoña Salamanca-Miño

    (Departamento de Estadística e I.O., Universidad de Sevilla, 41012 Seville, Spain
    These authors contributed equally to this work.)

Abstract

We study the distribution theory of some statistics related to records from a sequence of geometrically distributed random variables. The main novelty in this study is the introduction of q -calculus techniques. We obtain representations for the probability functions of some variables of interest, such as, for instance, record times, number of records, inter-record times, record indicators, etc., in terms of multiple q -integrals. It is remarkable to note that the expressions thus obtained are q -analogues of the corresponding well-known results in the absolutely continuous case. We also explore a duality between the results in the case of weak and ordinary records.

Suggested Citation

  • Fernando López-Blázquez & Begoña Salamanca-Miño, 2022. "Multiple q -Integral and Records from Geometrically Distributed Sequences," Mathematics, MDPI, vol. 10(13), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2313-:d:854139
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    References listed on IDEAS

    as
    1. Eric S. Key, 2005. "On the Number of Records in an iid Discrete Sequence," Journal of Theoretical Probability, Springer, vol. 18(1), pages 99-107, April.
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