Katarzyna Ostasiewicz

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There are various theoretical distributions which are used as models for the distribution of income. Among them the most commonly used is probably log-normal distribution, but also gamma distribution or log-logistic one. There are also a number of approximation methods of these distributions. The goodness of fit is commonly measured by mean squared deviation or value of X2 statistics. However, such measures of quality of approximation do not necessarily coincide with accuracy of some distribution characteristics, like inequality measures. The aim of this paper is to investigate the goodness of approximation of income distribution, given in the form of frequency distribution, by means of chosen theoretical distributions, namely, log-normal, gamma, log-logistic, Dagum and Singh-Maddala distribution. The goodness is measured both by mean squared error and deviation of some distribution characteristics. Values calculated on ungrouped data are used as a reference for comparisons.


theoretical income distribution; approximation of distribution; goodness of fit


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