Abstract
We continue the construction of goodness-of-fit tests resulting from characterizations via moments of the kth record values presented in [4] and [6]. Here we use U -statistics to estimate expectations appearing in the characterizations. We first state some characterizations. Let {Xn, n ≥ 1} be a sequence of independent and identically distributed (i.i.d.) random variables with continuous distribution function (c.d.f.) F and probability distribution function (p.d.f.) f . For a fixed integer k ≥ 1 we define the sequence Uk(1), Uk(2), . . . of kth (upper) record times of {Xn, n ≥ 1} as follows:
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