Analytical Methods in Probability Theory: Proceedings of the by Harald Bergström (auth.), Daniel Dugué, Eugene Lukacs, Vijay PDF

By Harald Bergström (auth.), Daniel Dugué, Eugene Lukacs, Vijay K. Rohatgi (eds.)

ISBN-10: 3540108238

ISBN-13: 9783540108238

ISBN-10: 3540367853

ISBN-13: 9783540367857

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Ser. A, p. 53-77. , theory of extreme order statistics, Wiley. 1971, Nonparametric methods in multivariate analysis, Wiley. , 1976, Asymptotic distributions tics, Ann. Statist. 4, p. 9]2-923. , 1973, Random variables, joint distribution functions and copulas, Kybernetika 9. , 1959, Bivariate extreme statistics, Ann. Inst. Stat. , 11, p. 199-210. , Reidel. , t. 45-55, 3e ~t. 92340 Bourg-la-Reine Universit~ Paris VI France 4, place Jussieu 75230 Paris Cedex 05 LOCAL L. I. and Resnick Department Institute Colorado University Xotterdam Fort of S t a t i s t i c s State University Collins A b s t r a c t .

Sider Let space (Xn) 0 be a m a r k o v (~ ,~ matrix (P(i,J))i, j 6 G (10) P(i, (if H(i) Using {i} ) >0 regularity (11) generated (9) and chain defined i+j) = H(i+j) i is n e v e r reached (10) f r o m 0) . We d e n o t e it is e a s i l y c h e c k e d ~(i, ~ ) that for e a c h n ) O is a r e g u l a r m a r t i n g a l e . f r o m the i n e q u a l i t y = lira (12) the n = 0,1, . . H(Xn+i)/H(Xn)< H(X n + i ) / H ( X n) n-~o~ exists probability s t a t e 0 and t r a n s i t i o n o( { j} )/H(i) .

O o o of the l a t t e r unit e x p o n e n t i a l d i s t r i b u t i o n . 4) More , Sn Yk:n quantile a standardized n Y. 1 ~ and the s t a n d a r d i z e d density for each < "'" < Y are the o r d e r s t a t i s t i c s of the above :n n:n sample. Now d e f i n e the e x p o n e n t i a l q u a n t i l e f u n c t i o n Qn(y) where . n . Exp(0,B) Then use we also Z where 0} B> for E x p o n e n t i a l i t y Sk ~ {~- ; k = 1 , 2 ..... n-l} n ..... s. O(n-½ log n) = ! S , we define the e s t i m a t e d n n of the family Exp(0,B) by .

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Analytical Methods in Probability Theory: Proceedings of the Conference Held at Oberwolfach, Germany, June 9–14, 1980 by Harald Bergström (auth.), Daniel Dugué, Eugene Lukacs, Vijay K. Rohatgi (eds.)


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