A Point Process Approach to Extreme Value Statistics

In Chap. 1 , some challenges to the problem of estimating extreme value distributions from limited amounts of data were discussed. In the current chapter, this problem will be approached by exploiting the concept of the mean upcrossing rate. It will be shown that this opens the door to very robust and reasonably accurate approximations to the extreme value distributions of stochastic processes, provided some reasonable conditions are satisfied. In the majority of books on extreme value statistics, which generally focus on asymptotic results for sequences of data, this approach is usually discussed under a heading that typically goes like the title of the current chapter. By stopping short of the asymptotic limits, this approach offers a uniquely applicable methodology for approximate extreme value analysis of a host of engineering problems.