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Testing a homogeneity of stochastic processes. (English) Zbl 1135.62066
Summary: This paper concentrates on modeling data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests for a detection of a change in an intensity of the Poisson process are described and illustrated by an example. We cover both the case when the time of the change is assumed to be known or unknown.

MSC:
62M07 Non-Markovian processes: hypothesis testing
62N05 Reliability and life testing
62N03 Testing in survival analysis and censored data
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