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A family of measures of uncertainty involving utilities: Definition, properties, applications and statistical inferences

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Abstract

Consider an experiment involving the observation of a discrete random variable, or quantitative classification process. When, in addition to the probability of each value or class we know its “utility” (or, more precisely, we can quantify the “nature” of each value or class), the “uncertainty corresponding to the utilities” may be evaluated. In this paper, we are first going to introduce a family of Measures of Uncertainty involving Utilities and several properties of this family are studied. Then, some immediate applications are discussed: the definition of criteria for Comparing Experiments in Statistical Decision problems, and the quantification of the Inequality with respect to an economical attribute or the Industrial Concentration. Finally, we will analyze the asymptotic behaviour of the measures in simple random sampling, and some related problems.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Oviedo, 33071, Oviedo, Spain

    Maria Angeles Gil, Rigoberto Perez &  Pedro Gil

Authors
  1. Maria Angeles Gil
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  2. Rigoberto Perez
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  3. Pedro Gil
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Additional information

This work was partially supported by the Comisión Asesora de Investigación Científica Técnica (CAICYT) under the contract PB85-0401.

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Gil, M.A., Perez, R. & Gil, P. A family of measures of uncertainty involving utilities: Definition, properties, applications and statistical inferences. Metrika 36, 129–147 (1989). https://doi.org/10.1007/BF02614085

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  • DOI: https://doi.org/10.1007/BF02614085

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