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Minimum dynamic discrimination information models

Part of: Probability theory on algebraic and topological structures Distribution theory - Probability Communication, information

Published online by Cambridge University Press:  14 July 2016

Majid Asadi ,
Nader Ebrahimi ,
G. G. Hamedani  and
Ehsan S. Soofi
Majid Asadi*
Affiliation:
University of Isfahan
Nader Ebrahimi*
Affiliation:
Northern Illinois University
G. G. Hamedani*
Affiliation:
Marquette University
Ehsan S. Soofi*
Affiliation:
University of Wisconsin-Milwaukee
*
∗Postal address: Department of Statistics, University of Isfahan, Isfahan, 81744, Iran. Email address: m.asadi@sci.ui.ac.ir
∗∗Postal address: Division of Statistics, Northern Illinois University, DeKalb, IL 60155, USA. Email address: nader@math.niu.edu
∗∗∗Postal address: Department of Mathematics, Statistics and Computer Science, Marquette University, PO Box 1881, Milwaukee, WI 53201-1881, USA. Email address: hosseinh@mscs.mu.edu
∗∗∗∗Postal address: School of Business Administration, University of Wisconsin-Milwaukee, PO Box 741, Milwaukee, WI 53201, USA. Email address: esoofi@uwm.edu
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Abstract

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In this paper, we introduce the minimum dynamic discrimination information (MDDI) approach to probability modeling. The MDDI model relative to a given distribution G is that which has least Kullback-Leibler information discrepancy relative to G, among all distributions satisfying some information constraints given in terms of residual moment inequalities, residual moment growth inequalities, or hazard rate growth inequalities. Our results lead to MDDI characterizations of many well-known lifetime models and to the development of some new models. Dynamic information constraints that characterize these models are tabulated. A result for characterizing distributions based on dynamic Rényi information divergence is also given.

Keywords

Lifetime distributionresidual life distributionmonotone densityfailure rate dominanceuncertainty ordering

MSC classification

Primary: 94A15: Information theory, general
Secondary: 60E15: Inequalities; stochastic orderings 60B05: Probability measures on topological spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 643 - 660
Copyright
© Applied Probability Trust 2005 

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