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Keywords:

  • semi-Markov process;
  • transition probabilities;
  • waiting time distributions;
  • evolution equation;
  • Monte Carlo simulation;
  • Saffir–Simpson scale;
  • hurricane derivatives;
  • Carvill index

ABSTRACT

The estimation of hurricane intensity evolution in some tropical and subtropical areas is a challenging problem. Indeed, the prevention and the quantification of possible damage provoked by destructive hurricanes are directly linked to this kind of prevision. For this purpose, hurricane derivatives have been recently issued by the Chicago Mercantile Exchange, based on the so-called Carvill hurricane index.

In our paper, we adopt a parametric homogeneous semi-Markov approach. This model assumes that the lifespan of a hurricane can be described as a semi-Markov process and also it allows the more realistic assumption of time event dependence to be taken into consideration. The elapsed time between two consecutive events (waiting time distributions) is modeled through a best-fitting procedure on empirical data. We then determine the transition probabilities and so-called crossing states probabilities. We conclude with a Monte Carlo simulation and the model is validated through a large database containing real data coming from HURDAT. Copyright © 2012 John Wiley & Sons, Ltd.