Abstract
Different record achievements are fixed in many domains of human activities. This process very often happens with some rate of digitization (up to seconds, meters, or thousands of individuals) of the observed results. By the examples of exponential and geometrical distributions, it is shown how such a type of the transitions from continuous to discrete distributions may vary the numbers of the record values in the corresponding sequences of the random variables.
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B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, Records (Wiley, New York, 1998).
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V. B. Nevzorov, Records. Mathematical Theory (Fazis, Moscow, 2000; Am. Math. Soc., 2001), In Ser.: Translations of Mathematical Monographs, Vol.194.
W. Vervaat, “Limit theorems for records from discrete distributions,” Stochastic Process. Appl. 1, 317–334 (1973).
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Original Russian Text © V.B. Nevzorov, 2017, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2017, Vol. 62, No. 3, pp. 459–465.
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Nevzorov, V.B. Comparison of numbers of records in the sequences of discrete and continuous random variables. Vestnik St.Petersb. Univ.Math. 50, 282–286 (2017). https://doi.org/10.3103/S1063454117030116
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DOI: https://doi.org/10.3103/S1063454117030116