Loss Distributions

Krzysztof Burnecki, Adam Misiorek and Rafał Weron

MPRA Paper from University Library of Munich, Germany

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. 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.

Keywords: Loss distribution; Insurance risk model; Random variable generation; Goodness-of-fit testing; Mean excess function; Limited expected value function (search for similar items in EconPapers)
JEL-codes: C15 C46 G22 (search for similar items in EconPapers)
Date: 2010
New Economics Papers: this item is included in nep-ecm, nep-ias and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/22163/2/MPRA_paper_22163.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:22163

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().