Vincent average: Difference between revisions
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Vincentization <ref>{{cite web |url=http://psych.stanford.edu/~jlm/pdfs/GenestVincentizing.pdf |title=Vincentization Revisisited |last1=Genest |first1=Christian |publisher=The Annals of Statistics|volume=Vol 20 |number=2 |pages=1137-1142 |date|format=PDF|accessdate=27 July 2014}} |
Vincentization <ref>{{cite web |url=http://psych.stanford.edu/~jlm/pdfs/GenestVincentizing.pdf |title=Vincentization Revisisited |last1=Genest |first1=Christian |publisher=The Annals of Statistics|volume=Vol 20 |number=2 |pages=1137-1142 |date=1992 |format=PDF|accessdate=27 July 2014}} </ref>, 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 this century. 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. |
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</ref>, 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 this century. 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. |
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To cast it in its greatest generality, |
To cast it in its greatest generality, |
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Revision as of 00:28, 29 July 2014
Vincentization [1], 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 this century. 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
Fi-1(α) = inf{t∈ℝ: Fi(t) ≥α), 0 <a < 1
The Vincent average of the Fi's is then computed as
F-1(α) = ∑ E wiFi-1(α), 0 < a < 1 i= 1 to n.
where w1,..., wn are arbitrarily chosen nonnegative numbers summing up to 1.
References
- ^ Genest, Christian (1992). "Vincentization Revisisited" (PDF). The Annals of Statistics. pp. 1137–1142. Retrieved 27 July 2014.
1. Vincentization revisited, Genest T., The Annals of Statistics, 1992, Vol. 20, No. 2, 1137-1142