Abstract
Connections between the records in various models is discussed. Martingale properties for some sequences of random variables connected with the record moments in the Fα-scheme are established. Bibliography: 24 titles.
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Literature Cited
R. Ballerini and S. I. Resnick, “Embedding sequences of successive maxima in extremal processes with applications,”J. Appl. Prob.,24, 827–837 (1987).
K. N. Chandler, “The distribution and frequency of record values,”J. Roy. Statist. Soc.,B 14, 220–228 (1952).
P. Deheuvels, “On record times associated withkth extremes,” in:Proceedings of the 3rd Pannonian symposium on mathematical statistics, (Visegrad, Hungary, 13–18 Sept., 1982), Akadémiai Kiadó, Budapest (1984), pp. 43–51.
P. Deheuvels, “Strong approximations ofkth records andkth record times by Wiener processes,”Probab. Th. Rel. Fields,77, 195–209 (1988).
W. Dziubdziela and B. Kopocinski, “Limiting properties of thekth record values,”Zastosow. Mat.,15, No. 2, 187–190 (1976).
H. N. Nagaraya, “Record values and related statistics—a review,”Commun. Statist. Theory Math.,17, 2223–2238 (1988).
V. B. Nevzorov, “Two characterizations using records,” in:Lect. Notes Math., Vol. 1233 (1986), pp. 79–85.
D. Pfeifer, “Asymptotic expansions for the mean and variance of logarithmic interrecord times,”Methods Oper. Res.,39, 113–121 (1981).
D. Pfeifer, “A note on moments of certain record statistics,”Z. Wahr. verw. Geb.,66, 293–296 (1984).
D. Pfeifer, “Extremal processes, secretary problems and the 1/e law,”J. Appl. Probab.,27, 722–733 (1989).
D. Pfeifer, “Some remarks on the record Nevzorov model,”Adv. Appl. Probab.,23, No. 4, 823–834 (1991).
A. Renyi, “Theorie des elements saillants d'une suite d'observations,” in:Colloquium in Combinatorial Methods in Probability Theory (1962), pp. 104–117 (see also:Selected Papers of A. Renyi, Vol. 3, Akadémiai Kiadó, Budapest (1976), pp. 50–65).
R. W., Shorrock, “On record values and record times,”J. Appl. Probab.,9, No. 2, 316–326 (1972).
M. C. K. Yang, “On the distribution of the inter-record times in an increasing population,”J. Appl. Probab.,12, 148–154 (1975).
Ya. Galambos,The Asymptotic Theory of Extremal Order Statistics, Kriger Malabar, Florida (1984).
V. B. Nevzorov, “Record times in the case of nonidentically distributed random variables,”Teor. Veroyatn. Primen.,29, No. 4, 808–809 (1984); English transl. inTheory Probab. Appl.
V. B. Nevzorov, “On record times and interrecord times for sequences of nonidentically distributed random variables,”Zap. Nauchn. Semin. LOMI,142, 109–118 (1985).
V. B. Nevzorov, “Onkth-record times and their generalizations,”Zap. Nauchn. Semin. LOMI,153, 115–121 (1986).
V. B. Nevzorov, “Records,”Teor. Veroyatn. Primen.,32, No. 2, 219–251 (1987).
V. B. Nevzorov, “Moments of some random variables related with records,”Vestn. Leningr. Univ. Mat. Mekh. Astron., No. 8, 33–37 (1987).
V. B. Nevzorov, “Distributions ofk-records in the discrete case,”Zap. Nauchn. Semin. LOMI,158, 133–137 (1987).
V. B. Nevzorov, “Martingale methods of investigation of records,” in:Statistics and Control of Random Processes, Moscow (1989), pp. 133–137.
V. B. Nevzorov, “Generating functions fork-record times. Martingale approach,”Zap. Nauchn. Semin. LOMI,184, 208–214 (1990).
V. B. Nevzorov and A. V. Stepanov, “Records: martingale approach to calculation of moments,” in:Rings and Modules. Limit Theorems of Probability Theory, Issue 2, Leningrad State University, Leningrad (1988), pp. 171–181.
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 207, pp. 19–36, 1993.
Translated by A. Sudakov.
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Deheuvels, P., Nevzorov, V.B. Records in the Fα-scheme. I. Martingale properties. J Math Sci 81, 2368–2378 (1996). https://doi.org/10.1007/BF02362342
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DOI: https://doi.org/10.1007/BF02362342