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Journal of Mathematical Sciences

, Volume 238, Issue 4, pp 523–529 | Cite as

Estimates for Order Statistics in Terms of Quantiles

  • A. E. LitvakEmail author
  • K. Tikhomirov
Article
  • 8 Downloads

Let X1, . . .,Xn be independent nonnegative random variables with cumulative distribution functions F1, F2, . . . , Fn satisfying certain (rather mild) conditions. We show that the median of kth smallest order statistic of the vector (X1, . . . , Xn) is equivalent to the quantile of order (k − 1/2)/n with respect to the averaged distribution \( F=\frac{1}{n}\sum \limits_{i=1}^n{F}_i \).

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of AlbertaEdmontonCanada
  2. 2.Princeton UniversityPrincetonUSA

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