REFERENCES
T. Anderson, Statistical Analysis of Time Series [Russian translation], Mir, Moscow (1976).
H. Bateman and A. Erdelyi, Higher Transcendental Functions [Russian translation], Nauka, Moscow (1973, 1974).
P. Billingsley, Convergence of Probability Measures [Russian translation], Nauka, Moscow (1977).
I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Connected Variables [in Russian], Nauka, Moscow (1965).
I. A. Ibragimov and Yu. A. Rozanov, Gaussian Random Processes [in Russian], Mir, Moscow (1970).
M. R. Leadbetter, G. Lindgren, and H. Rootz’en, Extremes and Related Properties of Random Sequences and Processes [Russian translation], Mir, Moscow (1989).
B. V. Finkelshtein, “Limit distributions of terms of variational series of values, connected with the simple Markov chain,” Ukr. Mat. J., 7, No.3, 313–332 (1955).
A. Ya. Hinchin, “Mathematical methods of the theory of queueing,” Trudy Steklov Mat. Inst., 49 (1955).
M. R. Chernick, “A limit theorem for the maximum of autoregressive processes with uniform marginal distributions,” Ann. Probab., 9, No.1, 145–149 (1981).
W. Maurer and B. H. Margolin, “The multivariate inclusion-exclusion formula and order statistics from dependent variates,” Ann. Statist., 4, No.6, 1190–1199 (1976).
G. S. Watson, “Extreme values in samples from m-dependent stationary stochastic process,” Ann. Math. Statist., 4, 798–800 (1954).
Author information
Authors and Affiliations
Additional information
__________
Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 132–144, Perm, Russia, 2001.
Rights and permissions
About this article
Cite this article
Tikhov, M.S. Limit distributions of extreme order statistics of weakly dependent random variables. J Math Sci 127, 2125–2133 (2005). https://doi.org/10.1007/s10958-005-0173-4
Issue Date:
DOI: https://doi.org/10.1007/s10958-005-0173-4