### Abstract

Original language | English |
---|---|

Article number | 326579 |

Number of pages | 6 |

Journal | Journal of Probability and Statistics |

Volume | 2014 |

DOIs | |

Publication status | Published - 2014 |

MoE publication type | A1 Journal article-refereed |

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*Journal of Probability and Statistics*,

*2014*, [326579]. https://doi.org/10.1155/2014/326579

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*Journal of Probability and Statistics*, vol. 2014, 326579. https://doi.org/10.1155/2014/326579

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

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Defining sample quantiles by the true rank probability

AU - Makkonen, Lasse

AU - Pajari, M.

PY - 2014

Y1 - 2014

N2 - 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.

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.

U2 - 10.1155/2014/326579

DO - 10.1155/2014/326579

M3 - Article

VL - 2014

JO - Journal of Probability and Statistics

JF - Journal of Probability and Statistics

SN - 1687-952X

M1 - 326579

ER -