Vincent average explained

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\geq 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

F _{1,...,} F _{n} represent arbitrary (empirical or theoretical) distribution functions and define their corresponding quantile functions byF ^{-1} _{i} (\alpha) = inf \{t\in R : F _{i(t)\ge\alpha)} \}, 0 <\alpha\leq 1 .

The Vincent average of the

F _{i} 's is then computed asF ^{-1} (\alpha) = \sum w _{i} F ^{-1} _{i} (\alpha), 0 <\alpha\leq 1 , i = 1 ,\ldots,n

where the non-negative numbers

w _{1,...,w} _{n} have a sum of 1 .

Notes and References

1. Vincentization Revisited . Genest . Christian . The Annals of Statistics. 20 . 2 . 1137–1142 . 1992 . PDF. 5 Sep 2018.
2. Group Reaction Time Distributions and an Analysis of Distribution Statistics . Ratcliff . Roger . Psychological Bulletin. 86 . 3 . 446–461 . 1979 . 10.1037/0033-2909.86.3.446 . 451109 . 18 November 2016.
3. The function of the viborissae in the behavior of the white rat . Vincent . Burnham . Stella . Behavior Monographs. 1 . 1912.