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Transformation of the Pearson System with Special Reference to Type IV

  • K. O. Bowman
  • W. E. Dusenberry
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 17)

Summary

The Pearson system of distributions consists of several types, including beta, gamma, and F-ratio families. There are interrelations between types, resulting from non-linear transformation of the variates. A description of these interrelations is given along with a new transformation which carries Type IV family into distributions for which (√ß1, ß2) points lie in Type I region. The usefulness of the transformation is illustrated in an application where the percentage points of the moment estimator for the shape parameter of the gamma distribution are derived.

Key Words

Transformation Pearson system of curves 

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References

  1. [1]
    Bowman, K. O. and Shenton, L. R. (1973). Biometrika 60, 155–167.MathSciNetzbMATHGoogle Scholar
  2. [2]
    Bowman, K. O. (1973). Biometrika 60, 623–628.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Box, G. E. P. and Cox, D. R. (1964). J. R. Statist. Soc. B 26, 211–252.MathSciNetGoogle Scholar
  4. [4]
    Burr, I. W. (1942). Ann. Math. Statist. 13, 215–232.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    D’Agostino, R. (1970). Biometrika 57, 679–81.zbMATHGoogle Scholar
  6. [6]
    D’Agostino, R. and Pearson, E. S. (1973). Biometrika 60, 613–622.MathSciNetzbMATHGoogle Scholar
  7. [7]
    David, F. N. and Johnson, N. L. (1951). Biometrika 38, 43–57.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Dusenberry, W. E. and Bowman, K. O. (1973). ORNL Report No. 4876, Oak Ridge National Laboratory, Oak Ridge, Tennessee.Google Scholar
  9. [9]
    Elderton, W. P. and Johnson, N. L. (1969). Systems of Frequency Curves. Cambridge University Press, London.zbMATHCrossRefGoogle Scholar
  10. [10]
    Johnson, N. L. and Kotz, S. (1970). Distributions in Statistics, Continuous Univariate Distributions - 1. Houghton Mifflin, Boston, and John Wiley.Google Scholar
  11. [11]
    Pearson, E. S. (1963). Biometrika 50, 1 and 2, 95–112.Google Scholar
  12. [12]
    Pearson, E. S. (1965). Biometrika 52, 282–285.CrossRefGoogle Scholar
  13. [13]
    Pearson, K. (1895). Phil. Trans. Roy. Soc. London Ser. A 186, 343–414.CrossRefGoogle Scholar
  14. [14]
    Shenton, L. R. (1965). Georgia Ag. Exp. Sta. Tech. Bull. N.S. 50, pp. 1–48.Google Scholar
  15. [15]
    Shenton, L. R. and Bowman, K. O. (1975). Johnson’s SU and the skewness and kurtosis statistics. Jour. Amer. Statist. Assoc. (to appear).Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht-Holland 1975

Authors and Affiliations

  • K. O. Bowman
    • 1
  • W. E. Dusenberry
    • 2
  1. 1.Computer Sciences DivisionUnion Carbide CorporationOak RidgeUSA
  2. 2.Lilly Research LaboratoriesIndianapolisUSA

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