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Large deviation probabilities for order statistics

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  • Stephen A. Book

Abstract

Asymptotic representations are found for the large deviation probabilities that the nα‐th order statistic exceeds δ, where δ>α. The probabilities are first expressed in terms of the empirical distribution function, and then the 1960 theorem of Bahadur and Ranga Rao is applied. The result is then shown to be more precise than a logarithmic statement in a 1969 paper of Sievers dealing with the asymptotic relative efficiency of the sample median test.

Suggested Citation

  • Stephen A. Book, 1971. "Large deviation probabilities for order statistics," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 18(4), pages 521-523, December.
    • Handle: RePEc:wly:navlog:v:18:y:1971:i:4:p:521-523
    DOI: 10.1002/nav.3800180411
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