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Sample Quantiles in Statistical Packages
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.
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Cited by
Cornwell, W. K., Cornelissen, J. H. C., Amatangelo, K., Dorrepaal, E., Eviner, V. T., Godoy, O., Hobbie, S. E., Hoorens, B., Kurokawa, H., Pérez‐Harguindeguy, N., et al. (2008) · Ecology Letters · doi:10.1111/j.1461-0248.2008.01219.x · Cited by 2,855
fitdistrplus: An R Package for Fitting Distributions
Delignette-Muller, M. L., & Dutang, C. (2015) · Journal of Statistical Software · doi:10.18637/jss.v064.i04 · Cited by 2,383
Suurmond, R., van Rhee, H., & Hak, T. (2017) · Research Synthesis Methods · doi:10.1002/jrsm.1260 · Cited by 881
Accuracy assessment of digital elevation models by means of robust statistical methods
Höhle, J., & Höhle, M. (2009) · ISPRS Journal of Photogrammetry and Remote Sensing · doi:10.1016/j.isprsjprs.2009.02.003 · Cited by 743
Travison, T. G., Vesper, H. W., Orwoll, E., Wu, F., Kaufman, J. M., Wang, Y., Lapauw, B., Fiers, T., Matsumoto, A. M., & Bhasin, S. (2017) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/jc.2016-2935 · Cited by 326
Metadata
- Authors
- Hyndman, R. J., & Fan, Y.
- Venue
- The American Statistician
- Publisher
- Informa UK Limited
- Published
- 1996-11
- Volume
- 50
- Issue
- 4
- Pages
- 361-365
- ISSN
- 0003-1305 (ISSN-L)
- 1537-2731
- OpenAlex
- W1985710418
- Cited by
- 1,183
- References
- 0
- FWCI
- 0.79
- Type
- journal article
- Language
- en
- Open access
- closed
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- Hyndman, R. J., & Fan, Y. (1996). Sample Quantiles in Statistical Packages. The American Statistician. https://doi.org/10.1080/00031305.1996.10473566
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
