Estimating income inequality in the stratified sampling from complete data. I. The unbiased estimation and applications

In order to answer the problem of quantifying the degree of unequalness among the individual shares in the distribution of income, several authors proposed and characterized the well-known additively decomposable measures of relative income inequality. In a previous paper, Perez, Caso and Gil [12] verified that for a large uncensused population of income earners, the additively decomposable index of order — 1 may be readily and unbiasedly estimated from a sample drawn at random from it. The Part 1 of the present paper deals with the study of the precision of the unbiased estimators in the stratified samplings with and without replacement. Then, some applications are briefly discussed. The aim of the Second Part is to analyze the asymptotic distribution of the sample income inequality index and to select the suitable sample size to estimate the population index with a specified degree of precision.