On the order statistics from correlated normal distribution

Saha, Krishna Kanta (1996) On the order statistics from correlated normal distribution. Masters thesis, Memorial University of Newfoundland.

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Abstract

The inferences for the order statistics for normal random variables with a general correlation structure, where correlations can be unequal or equal, positive or negative are discussed in this thesis. Specifically, based on a small correlations approach, we, first, develop the joint density function of the order statistics under the general correlation set-up. We. then, provide an approximation for the distribution of a single order statistic under the same correlation set-up. Special attention is given to the derivations for the distributions of the maxima and minima. The computational aspects of the distribution of the maxima, for example, are discussed in details for the homoscedastic equi-correlation, homoscedastic unequal correlations, and heteroscedastic unequal correlations cases. The applications of the proposed small correlations approach to compute the percentile points of the maxima are shown for the homoscedastic correlated normal variables following a stationary auto-regressive process of order one, and for the heteroscedastic correlated normal variables following a nonstationary antedependence model. Furthermore, the small correlations approach for the maxima is compared with the Bonferroni bounds approximation for unequally homoscedastic and heteroscedastic correlated normal variables.

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