×

Some considerations on the generalized information. (Spanish. English summary) Zbl 0731.62028

Summary: This paper deals with M. H. De Groot’s information measure [Theory Decis. 17, 287-303 (1984; Zbl 0572.90010)] which generalizes the Kullback information when discrepancy between distributions is to be measured. We define the modal information as a particular generalized information, and apply it in order to prove that the main properties of Kullback information are not verified by the generalized De Groot measure.

MSC:

62B10 Statistical aspects of information-theoretic topics

Citations:

Zbl 0572.90010
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] CSISZAR, I. (1977): “Information Measures: A Critical Survey{”,Transactions of 7th Prague Conference on Information Theory, Stat, Decision Function, Random Processes 1974, Boston: Reidel Publications.} · Zbl 0401.94010
[2] DE GROOT, M. H. (1962): “Uncertainty, information and sequential experiments{”,Ann. Math. Statist., 33, 404–419.} · Zbl 0151.22803
[3] DE GROOT, M. H. (1984): “Changes in utility as information{”,Theory and Decision, 17, 287–303.} · Zbl 0572.90010
[4] GARCIA-CARRASCO, M. P. (1985): “Criterio de comparación de experimentos basado en la inforación generalizada{”,Trabajos de Estadística (pendiente de publicación).}
[5] GARCIA-CARRASCO, M. P. (1986a): “Distribuciones mínimo informativas, caso de espacio paramétrico discreto y finito{”,Qüestió, vol. 10, n.0 1, 7–12.}
[6] GARCIA-CARRASCO, M. P. (1986b): “Funciones de evaluación modales{”,Trabajos de Estadística (pendiente de aceptación).}
[7] KULLBACK, S. (1968): “Information Theory and Statistics{”,Dover Publications, New York.} · Zbl 0897.62003
[8] LINDLEY, D. V. (1956): “On a measure of the information provided by an experiment{”, Ann. Math. Statist, 27, 986–1005.} · Zbl 0073.14103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.