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We derive tests of fit from characterizations of continuous distributions via moments of the kth upper record values. 1. Characterization conditions via moments of record values. Let {Xn : n ≥ 1} be a sequence of i.i.d. random variables with cdf F and pdf f . For a fixed integer k ≥ 1 we define the sequence Uk(1), Uk(2), . . . of kth (upper) record times of X1,X2, . . . as follows: Uk(1) = 1, Uk(n) = min{j > Uk(n− 1) : Xj:j+k−1 > XUk(n−1):Uk(n−1)+k−1}, for n = 2, 3, . . . Write Y (k) n := XUk(n):Uk(n)+k−1, n ≥ 1. The sequence {Y (k) n : n ≥ 1} is called the sequence of kth (upper) record values of the above sequence. For convenience we also take Y (k) 0 = 0 and note that Y (k) 1 = X1:k = min(X1, . . . ,Xk) (cf. [3]). Thus the finite sequence X1, . . . ,Xk is enough to determine Y (k) 1 , whereas if n > 1 then in general an infinite sequence is needed for Y (k) n . We see that for k = 1, 2, . . . , the sequences {Y (k) n : n ≥ 1} of kth record values can be obtained from {Xn : n ≥ 1} by inspecting successively the samples X1, (X1,X2), (X1,X2,X3), and so on. For k = 1, Y (1) 1 = X1, and the following terms are obtained by looking at the maxima of the successive samples: Y (1) 2 is the first maximum that exceeds Y (1) 1 , Y (1) 3 is the 2000 Mathematics Subject Classification: Primary 62E10, 62F03.

Tests derived from characterizations in terms of moments of record values