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How often do we reject a superior value? (Extended abstract)

Abstract : Words $a_1 a_2 \ldots a_n$ with independent letters $a_k$ taken from the set of natural numbers, and a weight (probability) attached via the geometric distribution $pq^{i-1}(p+q=1)$ are considered. A consecutive record (motivated by the analysis of a skip list structure) can only advance from $k$ to $k+1$, thus ignoring perhaps some larger (=superior) values. We investigate the number of these rejected superior values. Further, we study the probability that there is a single consecutive maximum and show that (apart from fluctuations) it tends to a constant.
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Kamilla Oliver, Helmut Prodinger. How often do we reject a superior value? (Extended abstract). 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.741-752. ⟨hal-01215069⟩

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