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PROPERTIES FOR GENERALIZED CUMULATIVE PAST MEASURES OF INFORMATION

Part of: Survival analysis and censored data Communication, information Distribution theory - Probability

Published online by Cambridge University Press:  29 October 2018

Camilla Calì ,
Maria Longobardi  and
Jorge Navarro Open the ORCID record for Jorge Navarro [Opens in a new window]
Camilla Calì
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II Via Cintia, I-80126 Napoli, Italy E-mail: camilla.cali@unina.it
Maria Longobardi
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II Via Cintia, I-80126 Napoli, Italy E-mail: maria.longobardi@unina.it
Jorge Navarro
Affiliation:
Facultad de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain E-mail: jorgenav@um.es
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Abstract

The Shannon entropy based on the probability density function is a key information measure with applications in different areas. Some alternative information measures have been proposed in the literature. Two relevant ones are the cumulative residual entropy (based on the survival function) and the cumulative past entropy (based on the distribution function). Recently, some extensions of these measures have been proposed. Here, we obtain some properties for the generalized cumulative past entropy. In particular, we prove that it determines the underlying distribution. We also study this measure in coherent systems and a closely related generalized past cumulative Kerridge inaccuracy measure.

Keywords

Applied probabilityreliability theory

MSC classification

Primary: 94A17: Measures of information, entropy
Secondary: 62N05: Reliability and life testing 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 1 , January 2020 , pp. 92 - 111
Copyright
Copyright © Cambridge University Press 2018 

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