On k-th record times,record values and their moments |
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| Authors: | Milena Bieniek Dominik Szynal |
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| Affiliation: | 1. Department of Statistics and Econometrics, Faculty of Economics, Maria Curie-Sk?odowska University, pl. Marii Curie-Sk?odowskiej 5, 20-031 Lublin, Poland;2. Institute of Mathematics, Maria Curie-Sk?odowska University, pl. Marii Curie-Sk?odowskiej 1, 20-031 Lublin, Poland |
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| Abstract: | 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. |
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| Keywords: | k-th record values Stirling numbers of the first kind Moments Incomplete gamma and Polygamma functions Zeta function Harmonic numbers |
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