On the maximal value of the expectation of record numbers

Mathematics
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Abstract

There are n independent identically distributed random variables with a continuous distribution function. The problem considered is, getting sequentially the values of these variables and selecting one of them as an initial point, how we can maximize the expected number of records among the rest of this sequence of random variables (without knowledge of the future values).

Keywords

record times record values record indicators 

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References

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    M. Ahsanullah and V. B. Nevzorov, Ordered Random Variables (Nova Science, New York, 2001).MATHGoogle Scholar
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    C. Arnold, N. Balakrishnan, and H. N. Nagaraja, Records (Wiley, New York, 1998).CrossRefMATHGoogle Scholar
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    V. B. Nevzorov, Records. Mathematical Theory (FAZIS, Moscow, 2000) [in Russian].Google Scholar
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    S. M. Samuels and J. M. Steele, “Optimal sequential selection of a monotone sequence from a random sample,” Ann. Probab. 9, 937–947 (1981).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Allerton Press, Inc. 2014

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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