Distributions of risk functions for the Pareto model

In statistical decision theory the risk function quantifies the average performance of a decision over the sample space. The risk function, that depends on the parameter of the model, is often summarized by the Bayes risk, that is its expected value with respect to a design prior distribution assigned to the parameter. However, since expectation may not be an adequate synthesis of the random risk, we propose to examine the whole distribution of the risk function. Specifically we consider point and interval estimation for the two-parameters Pareto model. Using conjugate priors we derive closed-form expressions for both the expected value and the density functions of the risk of each parameter under suitable losses. Finally an application to wealth distribution is illustrated.