Faculty Publications

Title

Closure and monotonicity properties of nonhomogeneous poisson processes and record values

Document Type

Article

Journal/Book/Conference Title

Probability in the Engineering and Informational Sciences

Volume

2

Issue

4

First Page

475

Last Page

484

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. © 1988, Cambridge University Press. All rights reserved.

Original Publication Date

1-1-1988

DOI of published version

10.1017/S0269964800000188

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