Article
Multiple q-integral and records from geometrically distributed sequences
Author/s | López Blázquez, José Fernando
Salamanca Miño, Begoña |
Department | Universidad de Sevilla. Departamento de Estadística e Investigación Operativa |
Publication Date | 2022-07-01 |
Deposit Date | 2023-04-25 |
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 ... 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. |
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