**8. Conclusions**

The main goal for this research is to model the extreme damages in Kenya resulting from natural disasters by considering both occurrence and the magnitude of the events. The magnitude of the natural disasters was quantified in terms of the total number of people affected. We use Excess over Threshold modelling, where the extreme damages are identified as the points beyond a sufficiently high threshold. The choice of the threshold significantly affects the parameter estimates, so we use three methods to identify the threshold: mean excess plot, parameter stability plot and Gertensgarbe and Werner plot. The threshold is found to be at 50,000.

In order to capture both the frequency and magnitude of the natural disasters, we use Compound Extreme Value Distribution that was proposed by Liu et.al in 1980. We identify the distribution of the number of exceedances to be Negative Binomial Distribution, while that for the magnitude of the exceedances is approximated by a GPD. We estimate the parameters of the CEVD using maximum likelihood estimation. The log-likelihood function is not in closed form, so we use PWM to determine the starting value for the iterations. We then carry out goodness-of-fit tests using a two-sample Kolmogorov-Smrinov test and a two-sample Anderson-Darling Test. We find that the NB-GP CEVD is a good fit for the data.

Finally, we carry out a prediction study for the NB-GP CEVD. The probability of exceeding the threshold in any year is found to be 0.4. We also predict, with different levels of certainty, the minimum and maximum values expected to be exceeded and not to be exceeded, respectively in the event of the occurrence of an extreme damage. We study the accuracy of these predictions by comparing the predicted values to the actual maximum and minimum. We find that the proposed distribution tends to overestimate the minimum damage at all the certainty levels. On the other hand, the distribution tends to underestimate the maximum damage at *p*< 0*:*95 certainty levels, and overestimate them at *p* ≥0*:*99 levels. Generally, we find that the proposed distribution performs better at predicting the minimum damages among those exceeding the threshold, than it does for the corresponding maximum damages.

We conclude that the NB-GP CEVD is a good fit for the distribution of the extreme damages resulting from natural disaster in Kenya. It performs better at predicting the minimum value that is expected to be exceeded by extreme damages as compared to maximum damages expected not to be exceeded.
