A record-values property of a renewal process with random inspection time

Udo Kamps and Diana Rauwolf

Statistics & Probability Letters, 2023, vol. 195, issue C

Abstract: Within renewal processes, Liberman (1985) characterized a homogeneous Poisson process via the so-called order-statistics property. This result is generalized and, for renewal processes with a random inspection time, a related characterization is shown by means of a record-values property. The structure of the conditional joint distribution of the first n occurrence times of a renewal process given n occurrences up to a random time is studied, and several examples along with respective cross-references are given.

Keywords: Record values; Order-statistics property; Poisson process; Characterization; Weighted distribution; Liouville distribution (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109785

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