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Abstrakty
The asymptotic behavior of intermediate order statistics and record values for folded distributions is studied. The relation between the weak convergence of a distribution function FX and of its folded distribution function, F|X|, is revealed in the cases of intermediate order statistics and record values. Additionally, a few illustrative examples are provided.
Czasopismo
Rocznik
Tom
Strony
179--197
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
- Department of Mathematics, College of Science & Humanity Studies, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
- Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, Egypt
autor
- Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, Egypt
autor
- Department of Mathematics, Faculty of Science, Zagazig University Zagazig, Egypt
Bibliografia
- [1] M. Ahsanullah, Record Statistics, Nova Science, New York, 1995.
- [2] B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, Records, Wiley, New York, 1998.
- [3] A. A. Balkema and L. de Hann, Limit distributions for order statistics, I, Theory Probab. Appl. 23 (1978), 77-92.
- [4] A. A. Balkema and L. de Hann, Limit distributions for order statistics, Theory Probab. Appl.II. 23 (1978), 341-358.
- [5] H. M. Barakat, On the restricted convergence of the intermediate and central terms of order statistics, Pobab. Math. Statist. 23 (2003), 229-240.
- [6] H. M. Barakat, M. E. Ghitany and E. K. AL-Hussaini, Asymptotic distributions of OSs and record values under the Marshall-Olkin parameterization operation, Comm. Statist. Theory Methods 38 (2009), 2267-2273.
- [7] H. M. Barakat and M. H. Harpy, Asymptotic behavior of the records of multivariate random sequences in a norm sense, Math. Slovaca 70 (2020), 1457-1468.
- [8] H. M. Barakat and E. M. Nigm, Asymptotic distributions of order statistics and record values arising from the class of beta-generated distributions, Statistics 48 (2014), 1005-1012.
- [9] H. M. Barakat, E. M. Nigm and M. H. Harpy, Limit theorems of order statistics and record values from the gamma and Kumaraswamy-generated-distributions, Bull. Malays. Math. Sci. Soc. 40 (2017), 1055-1069.
- [10] H. M. Barakat and A. R. Omar, On limit distributions for intermediate order statistics under power normalization, Math. Methods. Statist. 20 (2011), 365-377.
- [11] H. M. Barakat, A. A. Semida and M. H. Harpy, Asymptotic maxima of folded distributions with application to the multivariate extreme theory, J. Comput. Appl. Math. 443 (2024), art. 115765, 13 pp.
- [12] K. N. Chandler, The distribution and frequency of record values, J. Roy. Statist. Soc. Ser. B 14 (1952), 220-228.
- [13] D. M. Chibisov, On limit distributions of order statistics, Theory Probab. Appl. 9 (1964), 142- 148.
- [14] M. Csörgõ and J. Steinebach, On the estimation of the adjustment coefficient in risk theory via intermediate order statistics, Insurance Math. Econom. 10 (1991), 37-50.
- [15] J. Galambos, The Asymptotic Theory of Extreme Order Statistics, 2nd ed., Wiley, New York, 1987.
- [16] N. L. Johnson, The folded normal distribution: accuracy of the estimation by maximum likelihood, Technometrics 4 (1962), 249-256.
- [17] M. R. Leadbetter, G. Lindgren and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983.
- [18] F. C. Leone, L. S. Nelson and R. B. Nottingham, The folded normal distribution, Technometrics 3 (1961), 543-550.
- [19] D. M. Mason, Laws of large numbers for sums of extreme values, Ann. Probab. 10 (1982), 750-764.
- [20] K. Mutangi and F. Matarise, On how to find the norming constants for the maxima of a folded normally distributed variable, J. Statist. Research 46 (2012), 31-35.
- [21] S. Nadarajah and S. A. A. Bakar, New folded models for the log-transformed Norwegian fire claim data, Comm. Statist. Theory Methods 44 (2015), 4408-4440.
- [22] L. S. Nelson, The folded normal distribution, J. Qual. Technol. 12 (1980), 236-238.
- [23] S. I. Resnick, Limit laws for record values, Stoch. Process. Appl. 1 (1973), 67-82.
- [24] N. V. Smirnov, Limit distributions for the terms of a variational series, Amer. Math. Soc. Transl. 67 (1952), 82-143.
- [25] J. L. Teugels, Limit theorems on order statistics, Ann. Probab. 9 (1981), 860-880.
- [26] C. Y. Wu, The types of limit distributions for terms of variational series, Sci. Sinica 15 (1966), 749-762.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-81a2b999-d218-421e-bcff-150bc9951cb9
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