Abstract
We investigate conditions in order to decide whether a given sequence of real numbers represents expected record values arising from an independent, identically distributed, sequence of real-valued random variables. The main result provides a necessary and sufficient condition, relating any expected record sequence with the Stieltjes moment problem. The results are proved by means of a useful transformation on random variables. Some properties of this mapping, and its inverse, are discussed in detail, and, under mild conditions, an explicit inversion formula for the random variable that admits a given expected record sequence is obtained.
Funding Statement
Work partially supported by the National and Kapodistrian University of Athens’ Research fund under Grant 70/4/5637.
Acknowledgments
I would like to thank A. Giannopoulos for helpful discussions that led to the results of Theorem 4.2. Thanks are also due to the Editor, Professor Haas, an Associate Editor, and two anonymous Reviewers, for careful reading of the manuscript, resulting to several corrections.
Citation
Nickos Papadatos. "Sequences of expected record values." Electron. J. Probab. 28 1 - 19, 2023. https://doi.org/10.1214/23-EJP1007
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