**4.2 Detection of heavy-tailed behaviour**

The statistical methods used in this project rely on the heavy-tailedness of the underlying distribution. We observed that the data is right skewed as the mean is

**Figure 2.** *Scatter plot of Annual Occurrence.*

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

**Figure 3.** *Scatter plot of Annual Impact.*

increase in the annual occurrences in the last 20 years. During this period, all the

A similar trend is observed for the impacts of the natural disasters, as shown in **Figure 1b**. Very few people were being affected in the years between 1964 and 1990. Then from 1990, the severity of the natural disasters increased and a lot more

We assumed that the annual occurrences are independent of each other as with is the case with annual impact. We also assumed that the occurrences and impact are independent of each other. We can observe that the scatter plots 2,3 and 4 indicate that there is no serious violation of these assumptions (**Figures 2**-4).

The statistical methods used in this project rely on the heavy-tailedness of the underlying distribution. We observed that the data is right skewed as the mean is

years have experienced at least two events.

*Distribution of Natural Disasters in Kenya in the period: 1964–2018.*

*Natural Hazards - Impacts, Adjustments and Resilience*

**4.1 Check for Independence assumption**

**4.2 Detection of heavy-tailed behaviour**

people were being affected.

**Figure 1.**

**Figure 2.**

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*Scatter plot of Annual Occurrence.*

**Figure 4.** *Scatter plot of Annual Occurrence against Annual Impact.*

**Figure 5.** *Mean Excess Plot.*

**Figure 6.** *Exponential Q-Q plot.*

greater than the median (**Table 1**), indicating that the underlying distribution has a long tail. We will further investigate this by plotting the empirical mean excess function against different threshold values. We test the assumption using an empirical mean excess plot.

**Figure 7.**

**Figure 8.**

**Figure 9.** *Gertensgarbe Plot.*

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*Parameter Stability Plot.*

*Mean residual Life Plot.*

*On Modelling Extreme Damages from Natural Disasters in Kenya*

*DOI: http://dx.doi.org/10.5772/intechopen.94578*

An upward trend in the mean excess plot indicates heavy-tailed behaviour, as explained in Section 4.2. From **Figure 5**, we can observe a general upwards trend in the graph, except for the area between one million and two million.

To get more conclusive results, we also plot an exponential Q-Q and observe the pattern of the points in relation to the straight line. Heavy-tailed behaviour will be indicated by a convex departure from the straight line as explained in Section 4.2. Shorter tailed-distribution will have a concave departure and if the data are a sample from an exponential distribution, the points should be approximately linear.

We can observe the convex behaviour of the exponential Q-Q plot in **Figure 6**. Thus, we can conclude that the underlying distribution is heavy-tailed.
