Statistical tests for underestimation of loss distributions from NatCat models

Mathias Raschke ()

Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, 2017, vol. 87, issue 2, No 34, 1258 pages

Abstract: Abstract In the (re)insurance industry, the risk from natural hazards such as earthquakes or floods is quantified by models for natural catastrophes, also called NatCat models. One important output of NatCat models is the distribution function for the annual maximum of loss occurrence. The opportunities to test this fully specified distribution with a statistical test are limited as only the m-largest annual maxima of loss occurrence are known for a sample of n years in most cases. Here, new test statistics are introduced to validate the NatCat models against underestimation. The basis is the transformation of the largest realisations by a conditional distribution of order statistics. The resulting realisations of a new random variable are independent, and their distribution is known if H 0 is correct. Feasibility test statistics are formulated. The most powerful of these is a linear combination of normally distributed random variables. It performs much better than the conventional Kolmogorov–Smirnov for the conditional distribution of the excess. Different issues and weak points of all test statistics are briefly discussed.

Keywords: Goodness-of-fit test; Statistical test; Catastrophe models; Natural catastrophes; Loss occurrence (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11069-017-2784-8

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