After this estimation of the occurrence and the amount processes, they can be combined
to simulate future rainfall using Eq. (2).
The simulated rainfall paths are used to compute the rainfall index. By repeating this
procedure, a distribution of the index is derived. Results show that the distribution is
not normal. Instead, the data is usually skewed and heavy-tailed. Hence, instead of the
Girsanov transform for a Brownian motion, we apply the Esscher transform since it is
valid for Lévy processes.