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To model statistical data coming from two di erent distributions, Cooray and Ananda [1] introduced a composite (two-spliced) Lognormal-Pareto model, that was further extended by Scollnik [9] and fitted to insurance data. Inspired by these studies, more general three-spliced composite models are considered in this work, built by joining three di erent distributions. In particular, the study is focused on the three-spliced Exponential-Lognormal-Pareto distribution. The main characteristics of this model, as well as statistical inference are discussed. The parameters estimation is illustrated on random generated data.

When data exhibit a high frequency of small to medium values and a low frequency of large values, fitting a classical distribution might fail. This is why spliced models defined from different distributions on distinct intervals are proposed in the literature. In contrast to the intensive study of two-spliced distributions, the case with more than two components is scarcely approached. In this paper, we focus on three-spliced distributions and on their ability to improve the modeling of extreme data. For this purpose, we consider a popular insurance data set related to Danish fire losses, to which we fit several three-spliced distributions; moreover, the results are compared to the best-fitted two-spliced distributions from previous studies. [ABSTRACT FROM AUTHOR]

To model statistical data coming from two different distributions, Cooray and Ananda [1] introduced a composite (two-spliced) Lognormal-Pareto model, that was further extended by Scollnik [9] and fitted to insurance data. Inspired by these studies, more general three-spliced composite models are considered in this work, built by joining three different distributions. In particular, the study is focused on the three-spliced Exponential-Lognormal-Pareto distribution. The main characteristics of this model, as well as statistical inference are discussed. The parameters estimation is illustrated on random generated data. [ABSTRACT FROM AUTHOR]

Introduced to model heavy-tailed actuarial loss data, the composite Lognormal–Pareto distribution is piecewise built from the Lognormal and Pareto densities defined on mutually disjoint intervals. When estimating its parameters, the main challenge is the estimation of the unknown threshold where the density form changes. Motivated by the uncertainty of this parameter, in this article we consider two different approaches: first, we assume that the threshold is modeled by a random variable, and second, by a fuzzy number. We compare these two approaches especially from the parameters estimation point of view, under the continuity condition. We also study in some detail what happens with the Lognormal–Pareto distribution and with some of its characteristics under the fuzzy threshold assumption. [ABSTRACT FROM AUTHOR]