Limit distributions of order statistics with random indices in a stationary Gaussian sequence |
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Authors: | H M Barakat E M Nigm E O Abo Zaid |
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Institution: | Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt |
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Abstract: | In this article, we study the limit distributions of the extreme, intermediate, and central order statistics (os) of a stationary Gaussian sequence under equi-correlated setup. When the random sample size is assumed to converge weakly and to be independent of the basic variables, the sufficient (and in some cases the necessary) conditions for the convergence are derived. Finally, we show that the obtained result for the maximum os, with random sample size, is also applicable in the case of the non constant correlation case. |
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Keywords: | Central order statistics Extremes Gaussian sequences Intermediate order statistics Random sample size |
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