Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate numerically an intractable normalizing constant. In such a setup, simulation-based estimation methods are an appealing alternative. The approximate maximum likelihood estimation (AMLE) approach is employed. It is a general method that can be applied to mixtures with any component densities, as long as simulation is feasible. The focus is on the dynamic lognormal-generalized Pareto distribution, and the Cram\'er - von Mises distance is used to measure the discrepancy between observed and simulated samples. After deriving the theoretical properties of the estimators, a hybrid procedure is developed, where standard maximum likelihood is first employed to determine the bounds of the uniform priors required as input for AMLE. Simulation experiments and two real-data applications suggest that this approach yields a major improvement with respect to standard maximum likelihood estimation.

翻译：具有动态权重的混合分布是建模具有重尾特征损失数据的高效方式。然而，这类模型的最大似然估计较为困难，主要源于需要数值评估难以处理的归一化常数。在此设定下，基于模拟的估计方法成为颇具吸引力的替代方案。本文采用近似最大似然估计方法，这是一种通用方法，只要模拟可行，即可应用于任意分量密度的混合分布。研究聚焦于动态对数正态-广义帕累托分布，并采用Cramér-von Mises距离度量观测样本与模拟样本之间的差异。在推导估计量的理论性质后，本文开发了一种混合流程：首先使用标准最大似然估计确定AMLE所需均匀先验的边界。模拟实验及两项实际数据应用表明，该方法相较于标准最大似然估计具有显著改进。