Danish fire insurance data: A review and additional analysis

Department of Mathematical Statistics and Actuarial Science, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, 9301, South Africa

^* Corresponding author: shongwesc@ufs.ac.za

Abstract

The Danish fire insurance data is one of the most recognised and well-known datasets in the empirical insurance claims literature. This dataset is used in many textbooks and articles to illustrate the analysis of fire insurance claims, more specifically in the application of heavy-tailed loss distributions and extreme value theory. In this paper, we provide a short review of publications that used the Danish fire insurance data and conduct an additional analysis. Our additional analysis on the Danish fire insurance data involves investigating the: (i) modality issue using appropriate statistical tests and software, (ii) k-means clustering pattern using different techniques, (iii) effect of using a splicing model on the data, and (iv) differences in results that we obtained as compared to what other cited researchers reported in their earlier publications. In short, the objective of this paper is to highlight the importance of the Danish fire claims dataset by showcasing different models where it has been used to verify certain hypotheses in the empirical actuarial field. Additional analyses are also conducted to illustrate its dense usefulness in the actuarial and extremes field, where real-life datasets are scarce because they are often subjected to a lot of proprietary and privacy laws.