About the return period of a catastrophe

Abstract. When a natural hazard event like an earthquake affects region and generates catastrophe (NatCat), the following questions arise: how often does such occur? What is its return period (RP)? We derive combined (CRP) from concept of extreme value statistics theory – pseudo-polar coordinates. A CRP (weighted) average local RP intensities. Since CRP's reciprocal expected exceedance frequency, testable. As we show, related to spatial characteristics NatCat-generating dependence corresponding block maxima (e.g., annual wind speed maximum). For this purpose, extend previous construction for max-stable random fields consider recent area function NatCat research. Based on CRP, also develop new method estimate risk via stochastic scaling historical intensities (represented by records measuring stations) averaging computed loss defined or (or reciprocal) loss. Our application example winter storms (extratropical cyclones) over Germany. analyze station data hazard, events, curve insured losses. The most destructive storm our observation 20 years Kyrill in 2002, with 16.97±1.75. CRPs could be successfully tested statistically. state that higher case than non-max-stable case. Max-stable means measure Kendall's τ) two stations has same as larger size, 10 100 since copula (the structure) remains same. However, decreases increasing size; statistical indicator confirms this. Such control not realized models science industry. compare estimates these.