Characterizations in a Random Record Model with a Nonidentically Distributed Initial Record

We consider a sequence, of random length M , of independent, continuous observations Xi, 1 ≤ i ≤ M,whereM is geometric,X1 has cumulative distribution function (CDF)G, andXi, i ≥ 2, have CDF F . LetN be the number of upper records and letRn, n ≥ 1, be thenth record value. We show thatN is independent ofF if and only ifG(x) = G0(F (x)) for some CDF G0, and that if E(|X2|) is finite then so is E(|Rn|), 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.