Simulations process clarification #24
Description
Understanding of sim approach: tool simulates from the fitted distribution as below, please clarify if this is not correct. We replicated the simulations code in our own R script to compare the results by peril and in total for one set of historical data. We get broadly the same freq and severity simulations, with bigger differences at the average and in the tail.
o The MLE(s) for the selected frequency distribution are derived from this historical loss counts data (in this case poisson distribution). 15,000 frequency simulations are derived from the fitted frequency distribution using the lambda derived.
o The MLE(s) for the selected severity distribution are derived from the historical scaled occurrence loss amounts (in this case lognormal distribution). The occurrence severity simulations are derived from the fitted severity distribution using the mu and sigma parameters derived. These occurrence severity simulations are assigned a simulation year corresponding to the distribution of frequency simulations. The occurrence severity simulations are then summed by simulation year to get the final aggregated severity simulations.
o The confidence internals are derived by bootstrapping. The historical loss counts by year are bootstrapped (sampling with replacement) 1,000 times to generate parameters outputs (in this case 1000 lambda parameters). For each of these parameters 1,000 frequency simulations are generated from the fitted frequency distribution. (1,000 x 1,000 total simulations). The historical scaled occurrence loss amounts are bootstrapped (sampling with replacement) 1,000 times to generate parameters outputs (in this case 1000 mu and sigma parameters). For each of these sets of parameters, severity simulations are generated from the fitted severity distribution corresponding to the distribution of frequency distributions (and aggregated if necessary). The metrics for each parameter set of simulations are derived. For each metric, the lower confidence interval is selected as the 2.5% percentile and the upper confidence interval as the 97.5% percentile of all outputs