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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
##### Keywords:
survival functions; Poisson shocks
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