Normal approximation for fire incident simulation using permanental Cox processes

TL;DR

This paper develops a Normal approximation method for estimating natural disaster counts, specifically fire incidents, using positively associated point processes with exponentially decaying spatial correlation, and applies it to Thai fire data.

Contribution

It extends Normal approximation bounds to permanental Cox processes and demonstrates their application to real-world fire incident data.

Findings

Effective Normal approximation for fire incident counts

Application to Thai fire data from 2007-2020

Improved risk estimation for natural disasters

Abstract

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