The Likelihood for a Two-Dimensional Poisson Exceedance Point Process Model

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Yun, Seok-Hoon

  • 발행 : 2008.09.30

초록

Extreme value inference deals with fitting the generalized extreme value distribution model and the generalized Pareto distribution model, which are recently combined to give a single model, namely a two-dimensional non-homogeneous Poisson exceedance point process model. In this paper, we extend the two-dimensional non-homogeneous Poisson process model to include non-stationary effect or dependence on covariates and then derive the likelihood for the extended model.

키워드

Generalized extreme value distribution;generalized Pareto distribution;exceedance point process;non-homogeneous Poisson process

참고문헌

  1. von Mises, R. (1936). La distribution de la plus grande de valeurs, Reprinted in Selected Papers II, American Mathematical Society, Providence (1954), 271-294
  2. Smith, R. L. (1989). Extreme value analysis of environmental time series: an application to trend detection in ground-level ozone (with discussion), Statistical Science, 4, 367-393 https://doi.org/10.1214/ss/1177012400
  3. Leadbetter, M. R., Lindgren, G. and Rootzen, H. (1983). Extremes and Related Properties of Random Sequences and Processes, Springer, New York
  4. Pickands, J. (1975). Statistical inference using extreme order statistics, Annals of Statistics, 3, 119-131 https://doi.org/10.1214/aos/1176343003
  5. Resnick, S. (1987). Extreme Values, Point Processes, and Regular Variation, Springer, New York
  6. Fisher, R. A. and Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proceedings of the Cambridge Philosophical Society, 24, 180-190
  7. Gnedenko, B. V. (1943). Sur la distribution limite du terme maximum d'une serie aleatoire, Annals of Mathematics, 44, 423-453 https://doi.org/10.2307/1968974