Characterizations using record moments in a random record model and applications

We consider a random record model from a continuous parent X with cumulative distribution function F, where the number of available observations is geometrically distributed. We show that, if E(\X\) is finite, then so is E(\R-n\) whenever R-n, the nth upper record value, exists. We prove that appropriately chosen subsequences of E(R-n) characterize F and subsequences of E(R-n - Rn-1) identify F up to a location shift. We discuss some applications to the identification of wage-offer distributions in job search models.