*On Modelling Extreme Damages from Natural Disasters in Kenya DOI: http://dx.doi.org/10.5772/intechopen.94578*


**Table 9.**

The test-statistic

*Goodness-of-fit Test results.*

**Table 8.**

**7.3 Prediction study**

predicted using:

**292**

disasters in Kenya follow a NB-GP CEVD.

*Natural Hazards - Impacts, Adjustments and Resilience*

*<sup>x</sup>*^*<sup>p</sup>* <sup>¼</sup> <sup>50000</sup> <sup>þ</sup> *<sup>σ</sup>*^

*Dm*,*<sup>n</sup>* ¼ 0*:*3010 <0*:*3239 (35)

3 5

� 1

9 = ;

*ζ*

� 1

9 = ;

(36)

(37)

so we fail to reject the null hypothesis. We conclude that the data of natural

**Test statistic p-value** Kolmogorov–Smirnov 0.3010 0.0375 Anderson-Darling 2.8140 0.0346

From the estimation results in **Table 7**, we can tell that the probability of damages exceeding 50,000 in any year is approximately 0.4. We now want to predict the expected maximum and minimum among those exceeding the threshold

Using Eq. (X), the minimum damage that is expected to be exceeded among

The corresponding minimum equation, *xp*,among those exceeding 50000 that is expected not to be exceeded at any given year under different probabilities can be

*a*^^*θ* <sup>1</sup> � ^*<sup>θ</sup>* � � ð Þ <sup>1</sup> � *<sup>p</sup>* �1*=α*^ � <sup>1</sup> � �

> *a*^^*θ* <sup>1</sup> � ^*<sup>θ</sup>* � � *<sup>p</sup>*ð Þ �1*=α*^ � <sup>1</sup>

" #*<sup>ζ</sup>*

in any year with different certainties as explained in section X.

^*ζ*

*<sup>x</sup>*^*<sup>p</sup>* <sup>¼</sup> <sup>50000</sup> <sup>þ</sup> *<sup>σ</sup>*^

0*:*9, 0*:*95, 0*:*99, 0*:*995, 0*:*999 are given in **Table 9**.

those exceeding the threshold with probability p, is predicted using:

2 4

^*ζ*

Using the parameter estimates in **Table 7**, the prediction results for *p* ¼

of the prediction by comparing the prediction results to the statistics of the

exceedances (**Table 10**). This can be done using two measures:

1.Absolute Error = Predicted Value - Actual Value

ActualValue

2.Relative Error = AbsoluteError

The predicted maximum damage increases as the probabilities increase while the predicted minimum damage decreases as the probabilities increase. In other words, the range becomes larger at higher certainty levels. We can determine the accuracy

From **Table 11**, all the error measurements for the minimum values are positive, suggesting that the predicted values are higher than the actual value. This implies that the NB-GP CEVD tends to overestimate the minimum damage among the exceedances in any given year. We can also observe how the relative minimum error for the the minimum damage decreases as the probability increases.

8 < :

8 < : *Prediction Results for Extreme Damages in Kenya.*


#### **Table 10.**

*Statistics of the Exceedances.*


#### **Table 11.**

*Prediction Accuracy for Extreme Damages.*

The Relative error is highest at 0,9 level of certainty and lowest at 0.999 certainty level. So, accuracy of the predictions increases as the level of certainty increases. Generally, the distribution performs well at predicting the minimum values of those exceeding the threshold.

For the maximum values, the predicted values are lower than the actual values at 0.9 and 0.95 probabilities, and higher at *p*≥ 0*:*99. So, the proposed distribution underestimates the maximum values at probability levels less than 0.95, and overestimates them at probability levels greater than 0.95. In addition, the relative maximum errors are smaller when the predicted values are lower than the actual ones, as compared to when they are greater. So, the distribution overestimates the maximum values by a greater margin than it tends to underestimate. IN general, the NB-GP CEVD performs poorly at predicting the maximum values of the damages exceeding the threshold.

In overall, the absolute errors are smaller for the minimum values than the maximum values. This implies that the NB-GPD CEVD performs better at predicting the minimum values among those exceeding the threshold, than it does for the maximum values.
