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Variants of the Choquet–Deny theorem with applications

Part of: Distribution theory - Probability Special processes Multivariate analysis

Published online by Cambridge University Press:  14 July 2016

E. B. Fosam  and
D. N. Shanbhag
E. B. Fosam*
Affiliation:
Sheffield Hallam University
D. N. Shanbhag*
Affiliation:
Sheffield University
*
∗Postal address: School of Computing and Management Sciences, Sheffield Hallam University, 100 Napier Street, Sheffield S11 8HD, UK.
∗∗Postal address: School of Mathematics and Statistics, The University, Sheffield S3 7RH, UK.
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Abstract

A characterization of the exponential distribution based on a relevation-type equation and its discrete version are extended to the case of multidimensional spaces via variants of the Choquet–Deny theorem. Comments on some recent results in the literature are made.

Keywords

CHOQUET–DENY THEOREMEXPONENTIAL DISTRIBUTIONRELIABILITYRENEWAL PROCESS

MSC classification

Primary: 60E10: Characteristic functions; other transforms 62H10: Distribution of statistics
Secondary: 60K10: Applications (reliability, demand theory, etc.) 60E05: Distributions
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 101 - 106
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

This research was supported partly by US Army Grant DAAH-04–93-G-0030.

References

Chen, Y. H. (1994) Classes of life distributions and renewal counting process. J. Appl. Prob. 31, 1110–1115.Google Scholar
Dimitrov, B. and Khalil, Z. (1990) On a new characterization of the exponential distribution related to a queueing system with an unreliable server. J. Appl. Prob. 27, 221–226.CrossRefGoogle Scholar
Galambos, J. and Hagwood, C. (1994) An unreliable server characterization of the exponential distribution. J. Appl. Prob. 31, 274–279.Google Scholar
Huang, W. J. and Shoung, J. M. (1993) Some characterizations of the exponential and geometric distribution arising in queueing systems with an unreliable server. J. Appl. Prob. 30, 985–990.Google Scholar
Kakosyan, A. V., Klebanov, L. B. and Melamed, J. A. (1984) Characterization of Distributions by the Method of Intensively Monotonic Operators. (Lecture Notes in Mathematics 1088.) Springer, New York.Google Scholar
Lau, K. S. and Rao, B. L. S. P. (1990) Characterization of the exponential distribution by the relevation transform. J. Appl. Prob. 27, 726–729.Google Scholar
Lau, K. S. and Rao, B. L. S. P. (1992) Characterization of the exponential distribution by the relevation transform. J. Appl. Prob. 29, 1003–1004.Google Scholar
Rao, C. R. and Shanbhag, D. N. (1986) Recent results on characterization of probability distributions: A unified approach through extensions of Deny's thoerem. Adv. Appl. Prob. 18, 660–678.Google Scholar
Rao, C. R. and Shanbhag, D. N. (1989) Further extensions of the Choquet-Deny and Deny theorems with applications in characterization theory. Quart. J. Math. Oxford. 40, 333–350.Google Scholar
Rao, C. R. and Shanbhag, D. N. (1991) An elementary proof for an extended version of the Choquet-Deny Theorem. J. Multivar. Anal. 38, 141–148.Google Scholar
Rao, C. R. and Shanbhag, D. N. (1994) Choquet-Deny Type Functional Equations with Applications to Stochastic Models. Wiley, New York.Google Scholar
Shanbhag, D. N. (1991) Review on Dimitrov and Khalil. Math. Rev. (91j: 60147), 5590.Google Scholar
Van Harn, K. and Steutel, F. W. (1991) On a characterization of the exponential distribution. J. Appl. Prob. 28, 947–949.Google Scholar