Abstract
A new mathematical model of record values, named confirmed records, is constructed. It is based on the notion of kth record values, which, in turn, is a generalization of ordinary mathematical records and extremal order statistics. Confirmed records are considered for arbitrary k = 1, 2, ... under the assumption that the original random variables X1, X2, ... are independent and have the same continuous distribution function. For new record values, two representations are obtained in the most important special cases where the original variables have the exponential and the uniform distribution. For uniform and exponential confirmed records, means and variances are found.
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