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d-records in geometrically distributed random variables

Abstract : We study d-records in sequences generated by independent geometric random variables and derive explicit and asymptotic formulæ for expectation and variance. Informally speaking, a d-record occurs, when one computes the d-largest values, and the variable maintaining it changes its value while the sequence is scanned from left to right. This is done for the "strict model," but a "weak model" is also briefly investigated. We also discuss the limit q → 1 (q the parameter of the geometric distribution), which leads to the model of random permutations.
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Submitted on : Thursday, March 20, 2014 - 8:33:00 AM
Last modification on : Wednesday, November 29, 2017 - 10:26:22 AM
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Helmut Prodinger. d-records in geometrically distributed random variables. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2006, Vol. 8, pp.273--283. ⟨10.46298/dmtcs.375⟩. ⟨hal-00961118⟩



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