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Composite lognormal-Pareto model with random threshold. (English) Zbl 1277.62258

Summary: This paper further considers the composite lognormal-Pareto model proposed by K. Cooray and M. M. A. Ananda [ibid. 2005, No. 5, 321–334 (2005; Zbl 1143.91027)] and suitably modified by D. P. M. Scollnik [ibid. 2007, No. 1, 20–33 (2007; Zbl 1146.91028)]. This model is based on a lognormal density up to an unknown threshold value and a Pareto density thereafter. Instead of using a single threshold value applying uniformly to the whole data set, the model proposed in the present paper allows for heterogeneity with respect to the threshold and let it vary among observations. Specifically, the threshold value for a particular observation is seen as the realization of a positive random variable and the mixed composite lognormal-Pareto model is obtained by averaging over the population of interest. The performance of the composite lognormal-Pareto model and of its mixed extension is compared using the well-known Danish fire losses data set.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62F10 Point estimation
62G32 Statistics of extreme values; tail inference
91B30 Risk theory, insurance (MSC2010)
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References:

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