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.
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