Limit theory for bivariate central and bivariate intermediate dual generalized order statistics

• Autorzy: Barakat H. M. , Abd Elgawad M. A. , Nigm E. M.
• Języki publikacji: EN

Abstrakty

EN

Burkschat et al. (2003) have introduced the concept of dual generalized order statistics (dgos) to unify several models that produce descendingly ordered random variables (rv’s) like reversed order statistics, lower k-records and lower Pfeifer records. In this paper we derive the limit distribution functions (df’s) of bivariate central and bivariate intermediate m-dgos. It is revealed that the convergence of the marginals of the m-dgos implies the convergence of the joint df. Moreover, we derive the conditions under which the asymptotic independence between the two marginals occurs.

Słowa kluczowe

EN

dual generalized order statistics; dual generalized central order statistics; dual generalized intermediate order statistics

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2015
• Tom: Vol. 35, Fasc. 2
• Strony: 267--284
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Barakat H. M.

• Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

autor

Abd Elgawad M. A.

• Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

autor

Nigm E. M.

• Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

Bibliografia

• [1] H. M. Barakat, Limit theory of generalized order statistics, J. Statist. Plann. Inference 137 (1) (2007), pp. 1-11.
• [2] H. M. Barakat, E. M. Nigm, and M. A. Abd Elgawad, Limit theory for bivariate extreme generalized order statistics and dual generalized order statistics, ALEA Lat. Am. J. Probab. Math. Stat. 11 (1) (2014), pp. 331-340.
• [3] H. M. Barakat, E. M. Nigm, and M. A. Abd Elgawad, Limit theory for joint generalized order statistics, REVSTAT 12 (3) (2014), pp. 199-220.
• [4] M. Burkschat, E. Cramer, and U. Kamps, Dual generalized order statistics, Metron 61 (1) (2003), pp. 13-26.
• [5] D. M. Chibisov, On limit distributions for order statistics, Theory Probab. Appl. 9 (1964), pp. 142-148.
• [6] E. Cramer, Contributions to generalized order statistics, Habilitationsschrift, Reprint, University of Oldenburg, 2003.
• [7] H. A. David and H. N. Nagaraja, Order Statistics, third edition, Wiley, 2003.
• [8] U. Kamps, A Concept of Generalized Order Statistics, Teubner, Stuttgart 1995.
• [9] D. M. Mason, Laws of large numbers for sums of extreme values, Ann. Probab. 10 (1982), pp. 750-764.
• [10] D. Nasri-Roudsari, Extreme value theory of generalized order statistics, J. Statist. Plann. Inference 55 (1996), pp. 281-297.
• [11] J. Pickands III, Statistical inference using extreme order statistics, Ann. Statist. 3 (1975), pp. 119-131.
• [12] N. V. Smirnov, Limit distribution for terms of a variational series, Amer. Math. Soc. Transl. Ser. 1 (11) (1952), pp. 82-143.
• [13] J. L. Teugels, Limit theorems on order statistics, Ann. Probab. 9 (1981), pp. 868-880.
• [14] C. Y. Wu, The types of limit distributions for terms of variational series, Sci. Sinica 15 (1966), pp. 749-762.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).