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A new model for data with structural change at threshold: composite exponential-lognormal model. (English) Zbl 07094535

Summary: It is important for an insurance company to predict the future claims in order to evaluate premiums, to determine the reserve necessary to meet its obligation and probabilities of ruin, etc. As claim data is highly positively skewed and has heavy tail, no standard parametric model seems to provide an acceptable fit to both small and large losses. Composite models that use one standard distribution up to a threshold and other standard distribution thereafter are developed and it is seen that these composite models provide a better fit than the standard models when claim data involve small and high claims.
As the data involving both small and high values might have an upper tail not as heavy tail as the existing composite models, in this study we introduce a new composite model called as exponential-lognormal that is one parameter exponential density up to a threshold and two parameter lognormal density thereafter. The proposed model is continuous for the values of the parameters satisfying the continuity and differentiability conditions at threshold. The basic properties of this composite exponential-lognormal model are provided. A simulation study is carried out in order to obtain the parameter estimations. The performance of this model is compared with some existing classical and composite models using a proxy data generated from exponential-lognormal model. The Danish fire loss data up to the 95th percentile is also used as the upper tail of the proposed model is not as heavy as the composite models developed before and the performance of the model is also examined using this data. It is concluded that when the upper tail of the data is not as heavy as the composite models developed before the proposed model might be used.

MSC:

47N30 Applications of operator theory in probability theory and statistics
62H10 Multivariate distribution of statistics
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