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A Note on the Residual Entropy Function

Published online by Cambridge University Press:  27 July 2009

Pietro Muliere ,
Giovanni Parmigiani  and
Nicholas G. Polson
Pietro Muliere
Affiliation:
Dipartimento di Economia Politica e Metodi Quantitativi, Università di Pavia, via San Felice 5, Pavia, Italy, 27100
Giovanni Parmigiani
Affiliation:
Institute of Statistics and Decision Sciences, Duke University, Durham, North Carolina, 27708-0251
Nicholas G. Polson
Affiliation:
Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, Illinois 60637
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Abstract

Interest in the informational content of truncation motivates the study of the residual entropy function, that is, the entropy of a right truncated random variable as a function of the truncation point. In this note we show that, under mild regularity conditions, the residual entropy function characterizes the probability distribution. We also derive relationships among residual entropy, monotonicity of the failure rate, and stochastic dominance. Information theoretic measures of distances between distributions are also revisited from a similar perspective. In particular, we study the residual divergence between two positive random variables and investigate some of its monotonicity properties. The results are relevant to information theory, reliability theory, search problems, and experimental design.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 3 , July 1993 , pp. 413 - 420
Copyright
Copyright © Cambridge University Press 1993

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References

1.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. Probability models. New York: Holt Reinhardt and Winston.Google Scholar
2.Cover, T.M. & Thomas, J.A. (1991). Elements of information theory. New York: Wiley.Google Scholar
3.Gaede, K.-W. (1991). Stochastic orderings in reliability. In Mosler, K. & Scarsini, M.(eds.), Stochastic orders and decisions under risk. Hayward, CA: Institute of Mathematical Statistics, pp. 123–140.CrossRefGoogle Scholar
4.Kotlarski, I. (1972). Characterization of.probability distributions by conditional properties. Sankhya, A 34: 461–466.Google Scholar
5.Teitler, R., Rajagopal, A.K., & Ngai, U. (1986). Maximum entropy and reliability distributions. IEEE Transactions on Reliability R-35: 391–395.CrossRefGoogle Scholar
6.Verdugo Lazo, A.C.G. & Rathie, P.N. (1978). On the entropy of continuous probability distributions. IEEE Transactions on Information Theory IT24-1: 120–122.CrossRefGoogle Scholar