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Journal of Probability and Statistics
Volume 2014 (2014), Article ID 326579, 6 pages
Research Article

Defining Sample Quantiles by the True Rank Probability

1VTT Technical Research Centre of Finland, 02044 Espoo, Finland
2Berakon, Espoo, Finland

Received 30 June 2014; Revised 10 November 2014; Accepted 11 November 2014; Published 8 December 2014

Academic Editor: Z. D. Bai

Copyright © 2014 Lasse Makkonen and Matti Pajari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Many definitions exist for sample quantiles and are included in statistical software. The need to adopt a standard definition of sample quantiles has been recognized and different definitions have been compared in terms of satisfying some desirable properties, but no consensus has been found. We outline here that comparisons of the sample quantile definitions are irrelevant because the probabilities associated with order-ranked sample values are known exactly. Accordingly, the standard definition for sample quantiles should be based on the true rank probabilities. We show that this allows more accurate inference of the tails of the distribution, and thus improves estimation of the probability of extreme events.