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Estimating the number of natural disasters benefits the insurance industry interms of risk management. However, the estimation process is complicated due tothe fact that there are many factors affecting the number of such incidents. Inthis work, we propose a Normal approximation technique for associated pointprocesses for estimating the number of natural disasters under the followingtwo assumptions: 1) the incident counts in any two distinct areas arepositively associated and 2) the association between these counts in twodistinct areas decays exponentially with respect to distance outside some smalllocal neighborhood. Under the stated assumptions, we extend previous resultsfor the Normal approximation technique for associated point processes, i.e.,the establishment of non-asymptotic $L^1$ bounds for the functionals of theseprocesses [Wiroonsri (2019)]. Then we apply this new result to permanental Coxprocesses that are known to be positively associated. Finally, we apply ourNormal approximation results for permanental Cox processes to Thailand's firedata from 2007 to 2020, which was collected by the Geo-Informatics and SpaceTechnology Development Agency of Thailand.

Normal approximation for fire incident simulation using permanental Cox processes