Geodesic
d-records in geometrically distributed random variables
Discrete mathematics & theoretical computer science, Tome 8 (2006).

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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. 
@article{DMTCS_2006_8_a16,
     author = {Prodinger, Helmut},
     title = {d-records in geometrically distributed random variables},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {8},
     year = {2006},
     doi = {10.46298/dmtcs.375},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.375/}
}
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Prodinger, Helmut. d-records in geometrically distributed random variables. Discrete mathematics & theoretical computer science, Tome 8 (2006). doi : 10.46298/dmtcs.375. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.375/

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