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On the truncated composite Weibull–Pareto model. (English) Zbl 1199.60041

In view of applications in insurance the authors combine the Weibull and the Pareto distributions; the first one covers well the small losses up to a threshold, while the Pareto distribution covers the tails. The resulting composite distribution has a fatter tail than the Weibull distribution but thinner than the Pareto one. The density, the distribution function, the unique mode, the moments and the likelihood function of the composite distribution are studied in detail. The parameters are estimated by both the method of moments and maximum likelihood estimation.

MSC:

60E05 Probability distributions: general theory
62F10 Point estimation
62P05 Applications of statistics to actuarial sciences and financial mathematics
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