Burnecki, Krzysztof and Misiorek, Adam and Weron, Rafal (2010): Loss Distributions.

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Abstract
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. Goodnessoffit 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.
Item Type:  MPRA Paper 

Original Title:  Loss Distributions 
Language:  English 
Keywords:  Loss distribution; Insurance risk model; Random variable generation; Goodnessoffit testing; Mean excess function; Limited expected value function 
Subjects:  G  Financial Economics > G2  Financial Institutions and Services > G22  Insurance ; Insurance Companies ; Actuarial Studies C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions ; Specific Statistics C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General 
Item ID:  22163 
Depositing User:  Rafal Weron 
Date Deposited:  20. Apr 2010 10:14 
Last Modified:  03. Apr 2015 19:13 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/22163 