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Transformation of a Discrete Distribution to Near Normality

  • Fabián Hernández
  • Richard A. Johnson
Part of the NATO Advanced study Institutes Series book series (ASIC, volume 79)

Summary

Utilizing an information number approach, we propose an objective method for the normalization of either discrete distributions, or sample counts, by means of a power transformation. Approximations are also given to the original known probabilities. Next, we derive the large sample distribution of our estimate of the power transformation. We compare our methods with the Box-Cox procedure, applied to observed counts, and conclude that their technique often provides good approximations even though their underlying assumption of normality is clearly violated. Two examples illustrate our methods.

Key Words

Transformations discrete distributions 

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References

  1. Bartlett, M.S. (1947). The use of transformations. Biometrics, 3, 39–52.MathSciNetCrossRefGoogle Scholar
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  3. Ghiselli, E.E. (1964). Theory of Psychological Measurement. McGraw-Hill, New York.Google Scholar
  4. Hernandez, F., Johnson, R.A. (1979). Transformation of a discrete distribution to near normality. Technical Report No. 546, Department of Statistics, University of Wisconsin.Google Scholar
  5. Kullback, S. (1968). Information Theory and Statistics. Dover, New York.Google Scholar
  6. Tukey, J.W. (1977). Exploratory Data Analysis. Addison-Wesley, Reading, Massachusetts.zbMATHGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1981

Authors and Affiliations

  • Fabián Hernández
    • 1
    • 2
  • Richard A. Johnson
    • 1
  1. 1.University of WisconsinUSA
  2. 2.Dirección General de EstadisticaMexico

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