There are a large number of different definitions used for sample quantiles in statistical computer packages. Often within the same package one definition will be used to compute a quantile explicitly, while other definitions may be used when producing a boxplot, a probability plot, or a QQ plot. We compare the most commonly implemented sample quantile definitions by writing them in a common notation and investigating their motivation and some of their properties. We argue that there is a need to adopt a standard definition for sample quantiles so that the same answers are produced by different packages and within each package. We conclude by recommending that the median-unbiased estimator be used because it has most of the desirable properties of a quantile estimator and can be defined independently of the underlying distribution.
%0 Journal Article
%1 citeulike:1873437
%A Hyndman, Rob J.
%A Fan, Yanan
%D 1996
%I American Statistical Association
%J The American Statistician
%K 60-01-probability-instructional-exposition
%N 4
%P 361--365
%R 10.2307/2684934
%T Sample Quantiles in Statistical Packages
%U http://dx.doi.org/10.2307/2684934
%V 50
%X There are a large number of different definitions used for sample quantiles in statistical computer packages. Often within the same package one definition will be used to compute a quantile explicitly, while other definitions may be used when producing a boxplot, a probability plot, or a QQ plot. We compare the most commonly implemented sample quantile definitions by writing them in a common notation and investigating their motivation and some of their properties. We argue that there is a need to adopt a standard definition for sample quantiles so that the same answers are produced by different packages and within each package. We conclude by recommending that the median-unbiased estimator be used because it has most of the desirable properties of a quantile estimator and can be defined independently of the underlying distribution.
@article{citeulike:1873437,
abstract = {{There are a large number of different definitions used for sample quantiles in statistical computer packages. Often within the same package one definition will be used to compute a quantile explicitly, while other definitions may be used when producing a boxplot, a probability plot, or a QQ plot. We compare the most commonly implemented sample quantile definitions by writing them in a common notation and investigating their motivation and some of their properties. We argue that there is a need to adopt a standard definition for sample quantiles so that the same answers are produced by different packages and within each package. We conclude by recommending that the median-unbiased estimator be used because it has most of the desirable properties of a quantile estimator and can be defined independently of the underlying distribution.}},
added-at = {2017-06-29T07:13:07.000+0200},
author = {Hyndman, Rob J. and Fan, Yanan},
biburl = {https://www.bibsonomy.org/bibtex/2c1268b82a6a2ff24356d4464de461450/gdmcbain},
citeulike-article-id = {1873437},
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citeulike-linkout-0 = {http://dx.doi.org/10.2307/2684934},
citeulike-linkout-1 = {http://www.jstor.org/stable/2684934},
doi = {10.2307/2684934},
file = {hyndman_96_sample_33537.pdf},
interhash = {24c1a5aa5f2a2716c3eb5b274529a11b},
intrahash = {c1268b82a6a2ff24356d4464de461450},
issn = {00031305},
journal = {The American Statistician},
keywords = {60-01-probability-instructional-exposition},
month = nov,
number = 4,
pages = {361--365},
posted-at = {2008-03-04 04:03:55},
priority = {2},
publisher = {American Statistical Association},
timestamp = {2017-06-29T07:13:07.000+0200},
title = {{Sample Quantiles in Statistical Packages}},
url = {http://dx.doi.org/10.2307/2684934},
volume = 50,
year = 1996
}