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On composite lognormal-Pareto models. (English) Zbl 1146.91028

The author reviews three composite lognormal-Pareto models for using with the form of very highly positively skewed data that often arises in the actuarial and insurance industries. It is argued that the first model, proposed by K. Cooray and M. M. A. Ananda [Scand. Actuar. J. 2005, No. 5, 321–334 (2005; Zbl 1143.91027)], has a restrictive form due to its fixed mixing weights. The author proposes a second lognormal-Pareto composite model featuring mixing weights that were not fixed a priory as in the case of the first model. The third model is similar to the second one, but is constructed using a special case of the generalized Pareto distribution in place of the ordinary Pareto model. The illustrative example shows that the third model provided the best overall fit to the data and also guarded against overestimated probabilities of large losses.

MSC:

91B30 Risk theory, insurance (MSC2010)

Citations:

Zbl 1143.91027
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References:

[1] Cooray K., Scandinavian Actuarial Journal pp 321– (2005) · Zbl 1143.91027
[2] Klugman S.A., Loss Models: From data to decisions, 2. ed. (2004) · Zbl 1141.62343
[3] McNeil A.J., ASTIN Bulletin 27 pp 117– (1997)
[4] Resnick S.I., ASTIN Bulletin 27 pp 139– (1997)
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