50(4):361–365.

Paper doi abstract bibtex

Paper doi abstract bibtex

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{hyndmanSampleQuantilesStatistical1996, title = {Sample Quantiles in Statistical Packages}, author = {Hyndman, Rob J. and Fan, Yanan}, date = {1996-11}, journaltitle = {The American Statistician}, volume = {50}, pages = {361--365}, issn = {1537-2731}, doi = {10.1080/00031305.1996.10473566}, url = {https://doi.org/10.1080/00031305.1996.10473566}, 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.}, keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-12889338,~to-add-doi-URL,algorithms,comparison,definition,mathematical-reasoning,mathematics,robust-modelling,statistics}, number = {4} }

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