Modeling Data with Extreme Values Using Three-Spliced Distributions

When data exhibit a high frequency of small to medium values and a low frequency of large values, fitting a classical distribution might fail. This is why spliced models defined from different distributions on distinct intervals are proposed in the literature. In contrast to the intensive study of two-spliced distributions, the case with more than two components is scarcely approached. In this paper, we focus on three-spliced distributions and on their ability to improve the modeling of extreme data. For this purpose, we consider a popular insurance data set related to Danish fire losses, to which we fit several three-spliced distributions; moreover, the results are compared to the best-fitted two-spliced distributions from previous studies.