Something New, Something Old: Parametric Models for the Size of Distribution of Income

  • Robert F. Bordley
  • James B. McDonald
  • Anand Mantrala


Two new probability density functions (generalized beta and quadratic elasticity) are considered as models for the size distribution of income. The generalized beta distribution nests the generalized beta of the first and second kind, generalized gamma, lognormal and Pareto as well as introducing a number of new distributions to the literature. The quadratic elasticity distribution provides another generalization of the gamma distribution. The beta, gamma and lognormal distributions have been widely used in the income distribution literature. These distributions and many of their special cases are fit into five sets of US family income data for 1970, 1975, 1980, 1985, and 1990. This permits a comparison of the relative fit of several distributions over time.