Combinatorics of geometrically distributed random variables: Value and position of large left-to-right maxima (Q1613558)

Consider a sequence of \(n\) independent geometric random variables (rv) all with success probability \(p\). Such an rv is a left-to-right maximum if it is larger than all the previous ones, that is a record. Say that the last record is the instance \(r=1\), the previous record to that is instance \(r=2\), etc. For large \(n\) asymptotic formulas for the average value and position of the \(r\)th left-to-right maximum are derived using complex analytic methods on generating functions.