In applied statistics, Vincentization[1] was described by Ratcliff (1979),[2] and is named after biologist S. B. Vincent (1912),[3] who used something very similar to it for constructing learning curves at the beginning of the 1900s.
subjects' estimated or elicited quantile functions in order to define group quantiles from which
To cast it in its greatest generality, let
represent arbitrary (empirical or theoretical) distribution functions and define their corresponding quantile functions by The Vincent average of the
's is then computed as where the non-negative numbers