Defining sample quantiles by the true rank probability

Lasse Makkonen, M. Pajari

    Research output: Contribution to journalArticleScientificpeer-review

    5 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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    AU - Pajari, M.

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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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