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Preservation of certain classes of life distributions under Poisson shock models. (English) Zbl 0806.60075
Various survival functions both absolutely continuous and discrete are considered. The main point of interest is a survival function under the Poisson shocks. Let \(P_ k\) be the probability that a device survives the first \(k\) shocks which occur within the interval \((0,t)\). The author deals with properties of the survival function \(\sum^ \infty_{k = 0} P_ k {(\lambda t)^ k \over k!} e^{-\lambda t}\), \(t \geq 0,\) where \(\lambda\) is the intensity of the Poisson shocks process.

MSC:
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60E05 Probability distributions: general theory
90B25 Reliability, availability, maintenance, inspection in operations research
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