Vincent average

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. It basically consists of averaging n > 2 subjects' estimated or elicited quantile functions in order to define group quantiles from which F can be constructed.

To cast it in its greatest generality, let F₁,..., F_n represent arbitrary (empirical or theoretical) distribution functions and define their corresponding quantile functions by

${\displaystyle F_{i}^{-1}(\alpha )=\inf\{t\in \mathbb {R} :F_{i}(t)\geq \alpha )\},\quad 0<\alpha <1.}$

The Vincent average of the F_is is then computed as

${\displaystyle F^{-1}(\alpha )=\sum \mathbb {E} w_{i}F_{i}^{-1}(\alpha ),\quad 0<\alpha <1,\quad i=1,\ldots ,n}$

where the non-negative numbers w₁,..., w_n have a sum of 1.