Abstract

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.

摘要

引入到对重尾精算损失数据建模时，复合对数正态-帕累托分布是根据在相互不相交的区间上定义的对数正态和帕累托密度分段构建的。在估计其参数时，主要挑战是估计密度形式变化的未知阈值。由于该参数的不确定性，在本文中我们考虑了两种不同的方法：首先，我们假设阈值由随机变量建模，其次，由模糊数建模。我们比较了这两种方法，特别是从参数估计的角度，在连续性条件下。我们还详细研究了对数正态-帕累托分布及其在模糊阈值假设下的一些特征。