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Closure and Monotonicity Properties of Nonhomogeneous Poisson Processes and Record Values

Published online by Cambridge University Press:  27 July 2009

Ramesh C. Gupta  and
S.N.U.A. Kirmani
Ramesh C. Gupta
Affiliation:
Department of MathematicsUniversity of Maine, Orono, Maine 04469
S.N.U.A. Kirmani
Affiliation:
Department of Mathematics and Computer ScienceUniversity of Northern Iowa, Cedar Falls, Iowa 50614
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Abstract

Interconnections between occurrence times of nonhomogeneous Poisson processes, record values, minimal repair times, and the relevation transform are explained. A number of properties of the distributions of occurrence times and interoccurrence times of a nonhomogeneous Poisson process are proved when the mean-value function of the process is convex, starshaped, or superadditive. The same results hold for upper record values of independently identically distributed random variables from IFR, IFRA, and NBU distributions.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 4 , October 1988 , pp. 475 - 484
Copyright
Copyright © Cambridge University Press 1988

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