In this thesis we are going to use U.S. Census data to study median household income distribution for 13 U.S. counties and seven U.S. states. Over the years, researchers have fitted income data with various probability distributions. During our review of the literature, we saw that researchers do not agree on any one best

distribution.

We will be looking at lognormal, gamma and Weibull, each of which has two parameters. We will also investigate the Singh-Maddala, which has three parameters. Finally, we will introduce the Generalized Beta II, which has four parameters.

These distributions will be tested using Mean Squared Error, Mean Absolute Error, Chi-square Goodness-Of-Fit, Akaike's Information Criterion and Bayesian Information Criterion. We also use the graphical technique of QQ Plots.

We discover that the Singh-Maddala most often provides the best fit model for our income data, and we make the recommendation that users choose the Singh-Maddala distribution as their model when studying median household income distribution.