A New Model For Income Size Distributions

Abstract

After the well-known Pareto models, many probability-density functions have been proposed in the literature which are suitable for describing income size distribution. These specific functional forms can be grouped into three main categories: i) Functional forms, either proposed in order to describe the way income size distribution is produced, or based on stochastic processes, or deduced from probability arguments. The following contributions belong to this category: Vinci (1921), Amoroso (1924–25), Gibrat (1931), Champernowne (1952), Rutherford (1955), Mandelbrot (1960–62), Fisk (1961). ii) Functional forms which are proposed as phenomenological fits to the observed empirical distributions. In these category one should include the gamma-model proposed by Ammon (1895), March (1898) and Salem and Mount (1974); the beta-model suggested by Thurow (1970) and by Kakwani and Podder (1976); the Pearson V-kind distribution suggested by Vinci (1921); the Weibul distribution proposed by Bartles and Vanmetelen (1975); the Student log-t distribution studied by Kloek and Vandik (1976); the three-parameter lognormal distribution considered by Chieppa and Amato (1981); a gamma distribution generalized by Kloek and Vandik (1978) and Taille (1981), and the generalized beta distributions proposed by McDonald (1984). iii) Characterisations by means of differential equations, which are expected to reproduce the characteristics of regularity and conformity observed in the empirical income size distributions; the functional form is the solution of the corresponding differential equation. This group includes the models of Pareto (1896); the system of D’Addario (1949); some models of the system of Burr (1942); the model of Dagum (1977) and the model of Sinth and Maddala (1976).