Abstract

The inverse moment’s research can be used in many fields such as risk evaluation and insurance mathematics. In this paper, we consider the weighted inverse moment model based on asymptotically almost negatively associated (AANA, in short) sequences. Under some weak condition, we obtain the asymptotic approximation of inverse moments and its convergence rate. As applications of inverse moments, we study the random ratio models which contain the change-point detection models, and obtain the asymptotic moment approximation of random ratio and its convergence rate. Our conditions of inverse moment and random ratio models are very weaker than the existing models. In order to test our results, we do some simulations and real data analysis in this paper. Our results improve and general the existing works.

摘要

反矩的研究可应用于风险评估、保险数学等许多领域。在本文中，我们考虑基于渐近几乎负相关（简称 AANA）序列的加权反矩模型。在某些弱条件下，我们得到了反矩的渐近近似及其收敛速度。作为反矩的应用，我们研究了包含变点检测模型的随机比率模型，得到了随机比率的渐近矩近似及其收敛速度。我们的反矩和随机比率模型的条件比现有模型要弱得多。为了测试我们的结果，我们在本文中做了一些模拟和真实数据分析。我们的结果改进并概括了现有的工作。