Statistical Models for Exceedance Processes
In this chapter, Poisson processes and related processes are studied. These processes are essential for hydrological, environmental, financial and actuarial studies in Chapters 14 to 17. In Section 9.1 the basic concepts are introduced. We particularly mention the modeling of exceedances and exceedance times by means of Poisson processes. Within the framework of Poisson processes, we reconsider the concept of a T-year level in Section 9.2. The maximum likelihood and Bayesian estimation within models of Poisson processes is addressed in Section 9.3. The explanations about the GP approximation of exceedance dfs, cf. Section 6.5, will be continued within the framework of binomial and Poisson processes in Section 9.4. An extension of the modeling by Poisson processes from the homogeneous case to the inhomogeneous one is investigated in Section 9.5.
KeywordsPoisson Process Return Level Homogeneous Poisson Process Poisson Random Variable Exceedance Time
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