On \(k\)-th record times, record values and their moments. (English) Zbl 1331.62254
Summary: We give new formula for moments of \(k\)-th record values in terms of Stirling numbers of the first kind. In particular, the formulae allow to derive the explicit formulae for moments of \(k\)-th lower record values from exponential distribution which have not been known yet. Moreover, some interesting identities involving harmonic numbers are also obtained as corollaries to presented results.
MSC:
| 62G30 | Order statistics; empirical distribution functions |
| 60E05 | Probability distributions: general theory |
| 62E10 | Characterization and structure theory of statistical distributions |
Keywords:
\(k\)-th record values; Stirling numbers of the first kind; moments; incomplete gamma and polygamma functions; zeta function; harmonic numbersReferences:
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