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.


Poisson Process Return Level Homogeneous Poisson Process Poisson Random Variable Exceedance Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Todorovic, P. and Zelenhasic, E. (1970). A stochastic model for flood analysis. Water Resour. Res. 6, 1641–1648.Google Scholar
  2. 2.
    Hesselager, O. (1993). A class of conjugate priors with applications to excess-of-loss reinsurance. ASTIN Bulletin 23, 77–90.Google Scholar
  3. 5.
    Tsay, R.S. (1999). Extreme value analysis of financial data. Working paper, Graduate School of Business, University of Chicago; also see Section 7.7 in Tsay, R.S. (2002). Analysis of Financial Time Series. Wiley, New Jersey.Google Scholar

Copyright information

© Birkhäuser Verlag AG 2007

Personalised recommendations