American Statistician (1996), 50 361-365.
Rob J Hyndman1 and Yanan Fan2
- Department of Econometrics and Business Statistics, Monash University, Clayton VIC 3800, Australia.
- School of Mathematics and Statistics, University of NSW.
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 is used since it has most of the desirable properties of a quantile estimator and can be defined independently of the underlying distribution.
Keywords: sample quantiles, percentiles, quartiles, statistical computer packages.
R code: The quantile() function in R from version 2.0.0 onwards implements all the methods in this paper.
Errata:
- Table 1, p361. P2 should have lower bound equal to ⌊np⌋.
- p363, left column. P2 is satisfied if and only if α≥0 and β≤1.
Thanks to Eric Langford and Alan Dorfman for pointing out the errors. 8 May 2007.
Rob J Hyndman is
