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As the distribution function (d.f.) of the suitably normalized general intermediate (or central) term of order statistics converges on an interval [c, d] to an arbitrary nondecreasing function, the continuation of this (weak) convergence on the whole real line to an intermediate (or central) value distribution is proved.
Czasopismo
Rocznik
Tom
Strony
229--240
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Department of Statistics, Faculty of Science, Zagazig University, Egypt
Bibliografia
- [1] B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, A First Course in Order Statistics, Wiley, 1993.
- [2] A. A. Balkema and L. de Haan, Limit distributions for order statistics. I, Theory Probab. Appl. 23 (1978), pp. 77-92.
- [3] A. A. Balkema and L. de Haan, Limit distributions for order statistics. II, Theory Probab. Appl. 23 (1978), pp. 341-358.
- [4] H. M. Barakat, On the continuation of the limit distributions of the extreme and central terms of a sample, J. Spanish Society Statist. and O. R. (TEST) 6 (2) (1997), pp. 351-368.
- [5] H. M. Barakat, New versions of the extremal types theorem, South African Statist. J. 34 (1) (2000), pp. 1-20.
- [6] H. M. Barakat and B. Ramachandran, Continuability/Identifiability of local weak limits for certain normalized intermediate/central rank sequences of order statistics, J. Indian Statist. Assoc. 39 (2001), pp. 1-31.
- [7] D. M. Chibisov, On limit distributions of order statistics, Theory Probab. Appl. 9 (1964), pp. 142-148.
- [8] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2, Wiley, 1966 (Wiley Eastern University edition, 1979).
- [9] J. Galambos, The Asymptotic Theory of Extreme Order Statistics, 2nd edition, Krieger, FL, 1987.
- [10] J. Galambos, The development of the mathematical theory of extremes in the past half century, Theory Probab. Appl. 39 (2) (1995), pp. 142-148.
- [11] B. V. Gnedenko, On some stability theorems, in: Stability Problems for Stochastic Models. Proceedings of the 6th Seminar, Moscow, V. V. Kalashnikov and V. M. Zolotarev (Eds.), Lecture Notes in Math. 982, Springer, Berlin 1982, pp. 24-31.
- [12] B. V. Gnedenko and L. Senussi-Bereksi, On one characteristic of logistic distribution, Dokl. Akad. Nauk. SSSR (Soviet Mathematics) 267 (6) (1982), pp. 1293-1295.
- [13] B. V. Gnedenko and L. Senussi-Bereksi, On the continuation property of the limit distributions of maxima of variational series, Vestnik Moskov. Univ. Ser. Mat. Mekh., No. 3 (1983), pp. 11-20. Translation; Moscow Univ. Math. Bull., New York.
- [14] B. V. Gnedenko and L. Senussi-Bereksi, On one characteristic of the limit distributions for the maximum and minimum of variational series, Dokl. Akad. Nauk. SSSR (Soviet Mathematics), No. 5 (1983), pp. 1039-1040.
- [15] M. R. Leadbetter, G. Lindgren and H. Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer, 1983.
- [16] D. M. Mason, Laws of large numbers for sums of extreme values, Ann. Probab. 10 (1982), pp. 750-764.
- [17] J. Pickands, III, Statistical inference using extreme order statistics, Ann. Statist. 3 (1975), pp. 119-131.
- [18] H. J. Rossberg, Limit theorems involving restricted convergence, Theory Probab. Appl. 39 (2) (1995), pp. 98-314.
- [19] A. Shokry, On the limit theorems for the central terms of a variational series, Ph. D. Thesis, M.G.U., Moscow 1983.
- [20] N. V. Smirnov, Some remarks on limit laws for order statistics, Theory Probab. Appl. 12 (1967), pp. 337-339.
- [21] J. L. Teugels, Limit theorems on order statistics, Ann. Probab. 9 (1981), pp. 868-880.
- [22] C. Y. Wu, The types of limit distributions for some terms of variational series, Sci. Sinica 15 (1966), pp. 749-762.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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