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,..., Fn represent arbitrary (empirical or theoretical) distribution functions and define their corresponding quantile functions by

The Vincent average of the Fis is then computed as

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

References

  1. Genest, Christian (1992). "Vincentization Revisited" (PDF). 20 (2). The Annals of Statistics: 1137–1142. Retrieved 5 Sep 2018. Cite journal requires |journal= (help)
  2. Ratcliff, Roger (1979). "Group Reaction Time Distributions and an Analysis of Distribution Statistics" (PDF). 86 (3). Psychological Bulletin: 446–461. Retrieved 18 November 2016. Cite journal requires |journal= (help)
  3. Vincent, Stella; Burnham (1912). "The function of the viborissae in the behavior of the white rat". 1. Behavior Monographs. Cite journal requires |journal= (help)
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