Bayes-Verfahren zur Schätzung von Einkommensverteilungen

If the income scale is divided into k income ranges, the histogram form of the income distribution is completely determined by the k corresponding proportions. In section 2 Bayes estimators for these proportions are given for several loss functions and a special prior (Dirichlet-) distribution. The main purpose of this paper is the derivation of the linear Bayes estimator of section 3 without specifying a complete prior distribution. This linear Bayes estimator only depends on the first two moments of the prior distribution. It is shown that this estimator can be represented by a weighted average of the prior expected proportion and the maximum likelihood estimator