الفهرس 
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Abstract
Fitting a parametric model to income data can be a valuable and informative tool of distributional analysis. Not only can one summarize the information contained in thousands of observations, but also useful information can be drawn directly from the estimated parameters. Especially, if we interested in measuring income inequality, comparing different distributions or elaborating income redistribution policy: these concepts may sometimes be directly derived from parameters of a fitted distribution. Since the early work of Pareto (1895), a large number of models have been proposed to describe income distribution. The most frequently used in applied work are: Pareto, Lognormal (Gibrat 1931), Gamma (Salem and Mount, 1974), Burr III (Dagum 1977, Dagum 1980) and Burr XII (Singh and Maddala, 1976) models. The generalized beta distribution of first and second kind is also common used in practice (See: McDonald, 1984), which it includes as special cases most of the models for income distribution. All these functions constitute a set of possible statistical models for describing the income distribution. The four-parameter generalized Pareto introduced by Abd Elfattah, et al (2007) and some of its special cases are considered in this thesis as a new model for the distribution of income. The models considered are compared with four-parameter generalized beta of the first and second kind; respectively, and some of special and limiting cases. Maximum likelihood methods are used to estimate the parameters distributions with corresponding to some measures of goodness-of-fit. These measures identify the best-fitting for three and four-parameter for all models used. The total data income, especially, that concern of household’s income is used as a measure of income. The income data is applied on two countries; Egypt and United States.