*d*-records in geometrically distributed random variables

*Helmut Prodinger*

#### 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.Full Text: PDF PostScript