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Abstract:
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Let (X_i, Y_i), i=1,\ldots,n, be a random sample from a continuous bivariate distribution F(x,y) with positively associated components. Suppose the Y-concomitants of the top s order statistics of the X-sample values are observed. We are interested in the event that at least t of these concomitant values are among the top k values of the entire Y-sample. A closed form expression for the desired probability is derived using conditioning argument. It is shown that the desired probability depends on the population distribution, F(x,y), only through the associated copula function. Approximation of the desired probability for large samples is also explored. Finally application of these results to some real situations is discussed.
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