Email this article Estimates for Order Statistics in Terms of Quantiles
- Authors: Litvak A.E.1, Tikhomirov K.2
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Affiliations:
- University of Alberta
- Princeton University
- Issue: Vol 238, No 4 (2019)
- Pages: 523-529
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242553
- DOI: https://doi.org/10.1007/s10958-019-04254-5
- ID: 242553
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Abstract
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 \( F=\frac{1}{n}\sum \limits_{i=1}^n{F}_i \).
About the authors
A. E. Litvak
University of Alberta
Author for correspondence.
Email: aelitvak@gmail.com
Canada, Edmonton
K. Tikhomirov
Princeton University
Email: aelitvak@gmail.com
United States, Princeton
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