Keywords: Record times and values; distributional and limit results; inverse-transform and rejection methods; generation techniques; statistical tests.
@article{COMIM_2021_29_1_a8,
author = {Stepanov, Alexei},
title = {On the {Mathematical} {Theory} of {Records}},
journal = {Communications in Mathematics},
pages = {151--162},
year = {2021},
volume = {29},
number = {1},
mrnumber = {4251312},
zbl = {07413362},
language = {en},
url = {http://geodesic.mathdoc.fr/item/COMIM_2021_29_1_a8/}
}
Stepanov, Alexei. On the Mathematical Theory of Records. Communications in Mathematics, Tome 29 (2021) no. 1, pp. 151-162. http://geodesic.mathdoc.fr/item/COMIM_2021_29_1_a8/
[1] Ahsanullah, M., Nevzorov, V.B.: Records via Probability Theory. 2015, Springer, | MR
[2] Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: Records. 1998, John Wiley & Sons, New York, | MR
[3] Bairamov, I., Stepanov, A.: Numbers of near bivariate record-concomitant observations. J. Multivariate Anal., 102, 5, 2011, 908-917, Elsevier, | DOI | MR
[4] Balakrishnan, N., So, H.Y., Zhu, X.J.: On Box--Muller transformation and simulation of normal record data. Comm. Statist. Simulation Comput., 45, 10, 2016, 3670-3682, Taylor & Francis, | DOI | MR
[5] Balakrishnan, N., Pakes, A.G., Stepanov, A.: On the number and sum of near-record observations. Adv. in Appl. Probab., 37, 3, 2005, 765-780, Cambridge University Press, | DOI | MR
[6] Chandler, K.N.: The distribution and frequency of record values. J. Roy. Statist. Soc. Ser. B, 14, 2, 1952, 220-228, Wiley Online Library, | MR
[7] Foster, F.G., Stuart, A.: Distribution-free tests in time-series based on the breaking of records. J. Roy. Statist. Soc. Ser. B, 16, 1, 1954, 1-22, Wiley Online Library, | MR
[8] Foster, F.G., Teichroew, D.: A sampling experiment on the powers of the records tests for trend in a time series. J. Roy. Statist. Soc. Ser. B, 17, 1, 1955, 115-121, JSTOR, | MR
[9] Hashorva, E.: On the number of near-maximum insurance claim under dependence. Insurance Math. Econom., 32, 1, 2003, 37-49, Elsevier, | DOI | MR
[10] Hashorva, E., Hüsler, J.: The neighbourhood of the bivariate maxima: with application to insurance. In: IV International Conference in Stochastic Geometry, Convex Bodies, Empirical Measures & Applications to Engineering Science, Rend. Circ. Mat. Palermo (2) Suppl. part I, 70, 2002, 361-376, | MR
[11] Hashorva, E., Hüsler, J.: Estimation of tails and related quantities using the number of near-extremes. Comm. Statist. Theory Methods, 34, 2, 2005, 337-349, Taylor & Francis, | DOI | MR
[12] Nevzorov, V.B.: Records: Mathematical Theory. 2001, American Mathematical Society, Providence, | MR
[13] Nevzorov, V.B., Stepanov, A.: Records with confirmation. Statist. Probab. Lett., 95, 2014, 39-47, Elsevier, | DOI | MR
[14] Pakhteev, A., Stepanov, A.: Simulation of gamma records. Statist. Probab. Lett., 119, 2016, 204-212, Elsevier, | DOI | MR
[15] Pakhteev, A.I., Stepanov, A.V.: Generation of large sequences of normal record values and maxima. Vestnik St. Petersburg Univ. Math., 51, 3, 2018, 260-266, Springer, | MR
[16] Pakhteev, A., Stepanov, A.: Discrete records: Limit theorems for their spacings and generation methods. Statist. Probab. Lett., 148, 2019, 134-142, Elsevier, | DOI | MR
[17] Pakhteev, A., Stepanov, A.: On simulation of normal records. Comm. Statist. Simulation Comput., 48, 8, 2019, 2413-2424, Taylor & Francis, | MR
[18] Rényi, A.: On the extreme elements of observations. In: Selected papers of Alfred Rényi, 3, 1976, 50-65, Akademiai Kiado, Budapest, Translation of On the outliers of a series of observations (Hungarian), Magyar Tud. Akad. Mat. Fiz. Oszt. Kozl. 12 (1962) 105--121.. | MR
[19] Shorrock, R.W.: On record values and record times. J. Appl. Probability, 9, 2, 1972, 316-326, Cambridge University Press, | DOI | MR
[20] Stepanov, A.: On simulation of weak records. Comm. Statist. Simulation Comput., 48, 3, 2019, 797-806, Taylor & Francis, | DOI | MR
[21] Stepanov, A., Berred, A., Nevzorov, V.B.: Concomitants of records: limit results, generation techniques, correlation. Statist. Probab. Lett., 109, 2016, 184-188, Elsevier, | DOI | MR
[22] Tata, M.N.: On outstanding values in a sequence of random variables. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 12, 1969, 9-20, Springer, | DOI | MR
[23] Vervaat, W.: Limit theorems for records from discrete distributions. Stochastic Process. Appl., 1, 4, 1973, 317-334, Elsevier, | DOI | MR