Journal of applied mathematics & informatics
- Volume 18 Issue 1_2
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- Pages.247-259
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- 2005
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- 2734-1194(pISSN)
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- 2234-8417(eISSN)
A NOTE ON THE CONVERGENCE OF TRIVARIATE EXTREME ORDER STATISTICS AND EXTENSION
- BARAKAT H. M. (Department of Mathematics, Zagazing University) ;
- NIGM E. M. (Department of Mathematics, Zagazing University) ;
- ASKAR M. M. (Department of Mathematics, Zagazing University)
- Published : 2005.03.01
Abstract
Necessary and sufficient conditions, under which there exists (at least) a sequence of vectors of real numbers for which the distribution function (d.f.) of any vector of extreme order statistics converges to a non-degenerate limit, are derived. The interesting thing is that these conditions solely depend on the univariate marginals. Moreover, the limit splits into the product of the limit univariate marginals if all the bivariate marginals of the trivariate d.f., from which the sample is drawn, is of negative quadrant dependent random variables (r.v.'s). Finally, all these results are stated for the multivariate extremes with arbitrary dimensions.
Keywords
- Order statistics;
- trivariate extremes;
- convergence of multivariate extremes;
- negative quadrant random variables