Log-Skew-Normal and Log-Skew-t Distributions as Models for Family Income Data

  • Adelchi Azzalini
  • Thomas Del Cappello
  • Samuel Kotz


The U.S. family income data for the years 1970, 1975, 1978, 1980, 1985 and 1990 was fitted using the log-normal, Gamma, Singh-Maddala, Dagum type I and generalized Beta of second kind distributions, among others in earlier publications. Here we supplement these fittings by adding the log-skew-normal and log-skew-t distributions. In addition, we have performed similar numerical comparisons using 1997 income data collected in a sample survey from several European countries. The overall picture emerging from these numerical comparisons indicates that, while the log-skewed normal distribution provides a somewhat variable degree of goodness-of-fit, the log-skewed-t distribution seems to fit the data satisfactorily in a quite consistent way, and on the par with most creditable distributions.