Percentilrank

Percentilrank is a statistic that describes the relative position of a value within a distribution, expressed as a percentile. It indicates how a given observation compares to the rest of the data and is commonly reported as a value between 0 and 1 (often shown as a percentage between 0 and 100).

Calculation can follow two common approaches. The simplest definition uses the cumulative proportion: the percentile rank of a value x is the fraction of observations that are less than or equal to x, i.e., P(X ≤ x). In a dataset of n values, this yields a rank between 0 and 1 (or 0% to 100%). Some conventions handle ties by spreading or averaging positions, which can affect the exact result.

A second, widely used method is rank-based, exemplified by the PERCENT_RANK function found in many database systems. Here the rank R of a value within a partition is transformed by (R − 1) / (N − 1), where N is the number of rows in the partition. This yields a value in [0, 1], where identical values may receive identical or adjacent results depending on implementation.

Relation to percentile and quantile: a percentile is a value below which a given percentage of observations fall, while percentile rank describes the position of a specific value within the distribution. Different software packages may implement different interpolation or handling rules, so exact results can vary slightly.

Applications include comparing performance across datasets, non-parametric ranking, normalization and calibration of scores, and identifying outliers. In practice, percentilrank provides a scalable, non-parametric way to express relative standing without assuming a particular data distribution.