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• W1518075246 abstract "Let X,..., Xn be a sequence of dependent random variables from a continuous density function. Denote by X^ = min(Xi,... >Xn) and X(n) = max(Xi,... ,X?) the extreme order statistics. In this article Bonferroni-type inequalities and product-type approximations of order k > 1 are derived for the distribution and the moments of extreme order statistics for a sequence of stationary random variables. These results are particularized to m-spacings from a uniform distribution and moving sums of size m for independent normal random variables. These inequalities and approximations are compared with approximations and asymptotic results that have been previously derived. From the numerical results it is evident that there is merit in studying higher order Bonferroni-type inequalities and product-type approximations. The product-type approximations appear to be the most accurate approximations for the distribution and the moments of extreme order statistics." @default.
• W1518075246 created "2016-06-24" @default.
• W1518075246 creator A5035951768 @default.
• W1518075246 date "1992-01-01" @default.
• W1518075246 modified "2023-10-16" @default.
• W1518075246 title "Extreme order statistics for a sequence of dependent random variables" @default.
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• W1518075246 doi "https://doi.org/10.1214/lnms/1215461946" @default.
• W1518075246 hasPublicationYear "1992" @default.
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