Characterization of exponential distribution via regression of one record value on two non-adjacent record values

We characterize the exponential distribution as the only one which satisfies a regression condition. This condition involves the regression function of a fixed record value given two other record values, one of them being previous and the other next to the fixed record value, and none of them are adjacent. In particular, it turns out that the underlying distribution is exponential if and only if given the first and last record values, the expected value of the median in a sample of record values equals the sample midrange.Comment: To appear in Metrik

Goodness-of-fit tests via characterizations. General approach

K.W. Morris and D. Szyna

Limit theorems for the spacings of weak records

Let W(1), W(2), . . . be weak record values obtained from a sample of independent variables with common discrete distribution. In the present paper, we derive weak and strong limit theorems for the spacings W(n + m) - W(n), m a parts per thousand yen 1, n -> a