A family of measures of uncertainty involving utilities: Definition, properties, applications and statistical inferences
In order to incorporate the nature of the values of a variable into the measure of its uncertainty, the authors define a \(\beta\)-measure of uncertainty (called H for the purpose of this review) which can be viewed as a special case of the Kullback-Leibler information measure (for \(\beta =1)\) and of the non-additive directed divergences of order \(\beta\) (for \(\beta\neq 1)\). H depends not only on the (discrete set of) probabilities but also on the utilities, a term which is not necessarily used in the von Neumann-Morgenstern sense. A characterization of these \(\beta\)-measures is provided, and their properties are explored. Particular attention is paid to the use of such measures of uncertainty in the comparison of experiments in statistical decision problems, and in the quantification of inequality and industrial concentration. The asymptotic distribution of the measures is also examined, and large sample statistical inference explored.
scientific article; zbMATH DE number 4143222
scientific article