Vincent average

In applied statistics, Vincentization was described by Ratcliff (1979), and is named after biologist S. B. Vincent (1912), 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

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

The Vincent average of the F_is is then computed as

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

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