Let X1,X2,... be independent identically distributed (iid) random variables (rvs) with support on positive integers and (Wn,n[greater-or-equal, slanted]1) denote the corresponding sequence of weak record values. In the present paper we derive weak and strong limit theorems for the ratio of weak...

For a continuous distribution, F, it is well known that the sequence of kth-records is distributed as the sequence of 1st-record from 1-(1-F)k. This note shows that a similar result does not hold if the underlying distribution F is discrete.