Defined from different distributions on contiguous intervals, spliced distributions have been proposed with the purpose to better model extreme events in the presence of a high frequency of small to medium data. Therefore, a two-spliced distribution combines a heavy-tailed distribution above the threshold with a less heavy-tailed component below it. In contrast to the intensive study of two-spliced distributions, the case with more than two components is barely approached. In this chapter, we first present an overview of two-spliced distributions, then we introduce and study the three-spliced Gamma-Lognormal-Pareto distribution. We illustrate the estimation procedure in a simulation study, emphasizing the thresholds estimation.

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Extreme Values Modeling Using the Gamma-Lognormal-Pareto Three-Spliced Distribution

  • Adrian Bâcă,
  • Raluca Vernic

摘要

Defined from different distributions on contiguous intervals, spliced distributions have been proposed with the purpose to better model extreme events in the presence of a high frequency of small to medium data. Therefore, a two-spliced distribution combines a heavy-tailed distribution above the threshold with a less heavy-tailed component below it. In contrast to the intensive study of two-spliced distributions, the case with more than two components is barely approached. In this chapter, we first present an overview of two-spliced distributions, then we introduce and study the three-spliced Gamma-Lognormal-Pareto distribution. We illustrate the estimation procedure in a simulation study, emphasizing the thresholds estimation.