Defining sample quantiles by the true rank probability

Lasse Makkonen, M. Pajari

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

Abstract

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.
Original languageEnglish
Article number326579
Number of pages6
JournalJournal of Probability and Statistics
Volume2014
DOIs
Publication statusPublished - 2014
MoE publication typeA1 Journal article-refereed

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Sample Quantiles
Extreme Events
Statistical Software
Tail

Cite this

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Defining sample quantiles by the true rank probability. / Makkonen, Lasse; Pajari, M.

In: Journal of Probability and Statistics, Vol. 2014, 326579, 2014.

Research output: Contribution to journalArticleScientificpeer-review

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AB - 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.

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