Multiple q -Integral and Records from Geometrically Distributed Sequences

Fernando López-Blázquez and Begoña Salamanca-Miño
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Fernando López-Blázquez: Departamento de Estadística e I.O., Universidad de Sevilla, 41012 Seville, Spain
Begoña Salamanca-Miño: Departamento de Estadística e I.O., Universidad de Sevilla, 41012 Seville, Spain

Mathematics, 2022, vol. 10, issue 13, 1-17

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.

Keywords: weak and ordinary records; geometric distributions; Jackson integral; multiple q-integral; q-Stirling numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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