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)


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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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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