Characterizations in a Random Record Model with a Non-Identically Distributed Initial Record

We consider a sequence of random length M of independent absolutely continuous observations Xi, 1 <= i <= M, where M is geometric, X1 has cdf G, and Xi, i >= 2, have cdf F. Let N be the number of upper records and Rn, n >= 1, be the nth record value. We show that N is free of F if and only if G(x) = G0(F (x)) for some cdf G0 and that if E(|X2|) is finite so is E(|Rn|) for n >= 2 whenever N >= n or N = n. We prove that the distribution of N along with appropriately chosen subsequences of E(Rn) characterize F and G, and along with subsequences of E(Rn - Rn - 1) characterize F and G up to a common location shift. We discuss some applications to the identification of the wage offer distribution in job search models