This paper is intended as a guide to statistical inference for loss distributions. There are three basic approaches to deriving the loss distribution in an insurance risk model: empirical, analytical, and moment based. The empirical method is based on a sufficiently smooth and accurate estimate of the cumulative distribution function (cdf) and can be used only when large data sets are available. The analytical approach is probably the most often used in practice and certainly the most frequently adopted in the actuarial literature. It reduces to finding a suitable analytical expression which fits the observed data well and which is easy to handle. In some applications the exact shape of the loss distribution is not required. We may then use the moment based approach, which consists of estimating only the lowest characteristics (moments) of the distribution, like the mean and variance. Having a large collection of distributions to choose from, we need to narrow our selection to a single model and a unique parameter estimate. The type of the objective loss distribution can be easily selected by comparing the shapes of the empirical and theoretical mean excess functions. Goodness-of-fit can be verified by plotting the corresponding limited expected value functions. Finally, the hypothesis that the modeled random event is governed by a certain loss distribution can be statistically tested.
|Date of creation:||2010|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- L'Ecuyer, Pierre, 2004. "Random number generation," Papers 2004,21, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
- Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501, December.
- Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004.
"Simulation of risk processes,"
2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
- Burnecki, Krzysztof & Weron, Rafal, 2010. "Simulation of Risk Processes," MPRA Paper 25444, University Library of Munich, Germany.
- Burnecki, Krzysztof & Kukla, Grzegorz & Weron, Rafał, 2000. "Property insurance loss distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 269-278.
- Krzysztof Burnecki & Grzegorz Kukla & Rafal Weron, 2000. "Property insurance loss distributions," HSC Research Reports HSC/00/03, Hugo Steinhaus Center, Wroclaw University of Technology.
- Wolfgang Karl HÃ¤rdle & Yuichi Mori & JÃ¼rgen Symanzik, 2012. "Computational Statistics (Journal)," SFB 649 Discussion Papers SFB649DP2012-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
- Anna Chernobai & Krzysztof Burnecki & Svetlozar Rachev & Stefan Trück & Rafał Weron, 2006. "Modelling catastrophe claims with left-truncated severity distributions," Computational Statistics, Springer, vol. 21(3), pages 537-555, December.
- Krzysztof Burnecki & Rafal Weron, 2006. "Visualization tools for insurance risk processes," HSC Research Reports HSC/06/06, Hugo Steinhaus Center, Wroclaw University of Technology. Full references (including those not matched with items on IDEAS)