The present study introduces Dagum distribution Type I with three parameters and its properties. Maximum likelihood estimation method is used to estimate the model parameters. Income data for urban and rural sectors in Egypt for two periods of time: 2008/2009 and 2012/2013 are used. The fit of the Dagum distribution against the Burr Type XII and the lognormal with three parameters (3P) distributions is compared by using one-sample Kolmogorov-Smirnov test, and three other criteria for model selection: Akaike information, Bayesian information criteria and log likelihood index. Gini coefficient is used as a measure of income inequality, its observed value is compared with the estimated value for the three models of income.