| Title:
|
On the Mathematical Theory of Records (English) |
| Author:
|
Stepanov, Alexei |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
151-162 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present work, we briefly analyze the development of the mathematical theory of records. We first consider applications associated with records. We then view distributional and limit results for record values and times. We further present methods of generation of continuous records. In the end of this work, we discuss some tests based on records. (English) |
| Keyword:
|
Record times and values |
| Keyword:
|
distributional and limit results |
| Keyword:
|
inverse-transform and rejection methods |
| Keyword:
|
generation techniques |
| Keyword:
|
statistical tests. |
| MSC:
|
60G70 |
| MSC:
|
62G30 |
| idZBL:
|
Zbl 07413362 |
| idMR:
|
MR4251312 |
| . |
| Date available:
|
2021-07-09T12:41:16Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148996 |
| . |
| Reference:
|
[1] Ahsanullah, M., Nevzorov, V.B.: Records via Probability Theory.2015, Springer, MR 3379654 |
| Reference:
|
[2] Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: Records.1998, John Wiley & Sons, New York, MR 1628157 |
| Reference:
|
[3] Bairamov, I., Stepanov, A.: Numbers of near bivariate record-concomitant observations.J. Multivariate Anal., 102, 5, 2011, 908-917, Elsevier, MR 2776577, 10.1016/j.jmva.2011.01.007 |
| Reference:
|
[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, MR 3533612, 10.1080/03610918.2014.950872 |
| Reference:
|
[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, MR 2156559, 10.1239/aap/1127483746 |
| Reference:
|
[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 0053463 |
| Reference:
|
[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 0065123 |
| Reference:
|
[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 0073097 |
| Reference:
|
[9] Hashorva, E.: On the number of near-maximum insurance claim under dependence.Insurance Math. Econom., 32, 1, 2003, 37-49, Elsevier, MR 1958767, 10.1016/S0167-6687(02)00192-0 |
| Reference:
|
[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 1962578 |
| Reference:
|
[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, MR 2163357, 10.1081/STA-200047414 |
| Reference:
|
[12] Nevzorov, V.B.: Records: Mathematical Theory.2001, American Mathematical Society, Providence, MR 1791071 |
| Reference:
|
[13] Nevzorov, V.B., Stepanov, A.: Records with confirmation.Statist. Probab. Lett., 95, 2014, 39-47, Elsevier, MR 3262948, 10.1016/j.spl.2014.08.002 |
| Reference:
|
[14] Pakhteev, A., Stepanov, A.: Simulation of gamma records.Statist. Probab. Lett., 119, 2016, 204-212, Elsevier, MR 3555288, 10.1016/j.spl.2016.08.002 |
| Reference:
|
[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 3886024 |
| Reference:
|
[16] Pakhteev, A., Stepanov, A.: Discrete records: Limit theorems for their spacings and generation methods.Statist. Probab. Lett., 148, 2019, 134-142, Elsevier, MR 3905247, 10.1016/j.spl.2019.01.016 |
| Reference:
|
[17] Pakhteev, A., Stepanov, A.: On simulation of normal records.Comm. Statist. Simulation Comput., 48, 8, 2019, 2413-2424, Taylor & Francis, MR 3985816 |
| Reference:
|
[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 0157394 |
| Reference:
|
[19] Shorrock, R.W.: On record values and record times.J. Appl. Probability, 9, 2, 1972, 316-326, Cambridge University Press, MR 0350869, 10.2307/3212801 |
| Reference:
|
[20] Stepanov, A.: On simulation of weak records.Comm. Statist. Simulation Comput., 48, 3, 2019, 797-806, Taylor & Francis, MR 3938056, 10.1080/03610918.2017.1400051 |
| Reference:
|
[21] Stepanov, A., Berred, A., Nevzorov, V.B.: Concomitants of records: limit results, generation techniques, correlation.Statist. Probab. Lett., 109, 2016, 184-188, Elsevier, MR 3434976, 10.1016/j.spl.2015.11.020 |
| Reference:
|
[22] Tata, M.N.: On outstanding values in a sequence of random variables.Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 12, 1969, 9-20, Springer, MR 0247655, 10.1007/BF00538520 |
| Reference:
|
[23] Vervaat, W.: Limit theorems for records from discrete distributions.Stochastic Process. Appl., 1, 4, 1973, 317-334, Elsevier, MR 0362457, 10.1016/0304-4149(73)90015-X |
| . |
