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

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

2011-01-25

arxiv.org/abs/1101.4873v1

Mathematics

Probability

To appear in Metrika

Scientific paper

10.1007/s00184-011-0350-z

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.

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