Characterizations in a random record model with a nonidentically distributed initial record

We consider a sequence, of random length M, of independent, continuous observations X-i, 1 <= i <= M, where M is geometric, X-1 has cumulative distribution function (CDF) G, and X-i, i >= 2, have CDF F. Let N be the number of upper records and let R-n, n >= 1, be the nth record value. We show that N is independent of F if and only if G (x) = Go (F (x)) for some CDF G(0), and that if E(vertical bar X-2 vertical bar) is finite then so is E(vertical bar R-n vertical bar), n >= 2, whenever N > n or N = n. We prove that the distribution of N, along with appropriately chosen subsequences of E(R-n), characterize IT and G and, along with subsequences of E(R-n - 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.