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Working Paper, No. 2005-05, 2005
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  Rn1) 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.

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