A family of measures of uncertainty involving utilities: Definition, properties, applications and statistical inferences
type: Item
instance of: scholarly article
title: A family of measures of uncertainty involving utilities: Definition, properties, applications and statistical inferences
zbMATH Open document ID: 0697.62004
DOI: 10.1007/BF02614085
author: R. Perez
author: M. Ángeles Gil
author: Pedro Gil
published in: Metrika
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176224
review text: 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.
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 60A99
Mathematics Subject Classification ID: 62B15
zbMATH DE Number: 4143222
zbMATH Keywords: entropy
zbMATH Keywords: measure of uncertainty
zbMATH Keywords: Kullback-Leibler information measure
zbMATH Keywords: non-additive directed divergences
zbMATH Keywords: utilities
zbMATH Keywords: asymptotic distribution
zbMATH Keywords: large sample statistical inference
reviewed by: Andrew Dale
MaRDI profile type: Publication
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OpenAlex ID: W2060685049
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description: scientific article; zbMATH DE number 4143222