The Completeness and Uniqueness of Johnson's System in Skewness–Kurtosis Space

References

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• Slifker , J. F. and Shapiro , S. S. 1980 . The Johnson system: selection and parameter estimation . Technometrics , 22 ( 2 ) : 239 – 246 . Let x 3z , x z , x −z andx −3z be the values corresponding to 3z, z, −z, −3z under the Johnson transformation z = γ + δf((x − ξ)/λ), let m = x 3z  − x z , n = x −z  − x −3z andp = x z  − x −z . Then the ratio discriminates among the three distribution families: For S U , mn/p 2 > 1; for S B , mn/p 2 < 1; for S L , mn/p 2 = 1
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