quantiletype

Quantile type is a convention used in statistics to define how sample quantiles are estimated from a finite data sample. It specifies how the probability p in the interval (0, 1) is mapped to a position within the ordered data and how the corresponding quantile is computed, either by selecting a data point or by interpolating between adjacent order statistics. The concept was formalized by Rob Hyndman and Yingying Fan in 1996, who described nine distinct quantile types that are implemented in many statistical software packages.

The nine types differ in how they treat endpoints and interpolation, which can lead to different quantile estimates for the same data and probability. Some types rely on the inverse empirical distribution function with little or no interpolation, while others use linear interpolation between order statistics with varying weighting schemes. Type 7, which uses linear interpolation between neighboring order statistics with a specific indexing rule, is the default implementation in R’s quantile function and is widely used in practice. Other types (2 through 6, and 8–9) employ alternative rules for mapping p to data positions and handling ties or sample size effects.

Choice of quantile type can influence summary statistics such as quartiles and medians, and it may affect downstream analyses that rely on quantile-based metrics or visualizations like boxplots. Because software packages differ in the default type, practitioners often specify the type explicitly to ensure reproducibility when comparing results across tools.

See also: Hyndman–Fan quantile types, order statistics, empirical distribution function, quantile estimation.