Records from partial comparisons and discrete approximations
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In this paper we study records obtained from partial comparisons within a sequence of independent and identically distributed (i.i.d.) random variables, indexed by positive integers, with a common density f. Our main result is that if the comparison sets along a subsequence of the indices satisfy a certain compatibility property, then the corresponding record events are independent. Moreover, the record event probabilities do not depend on the density f and we obtain closed form expressions for the distribution of r^th record value for any integer r ≥ 1. Our proof techniques extend to the discrete case as well and we estimate the difference in record event probabilities associated with a continuous random variable X and its discrete approximations.
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