基于混合正态模型的糖尿病住院病人医疗保险设计

Design on A Medical Insurance Basing on Mix Normal Distributions Model for Inpatients with Diabetes

目的提出一种基于混合正态模型来拟合糖尿病住院病人风险损失规律的精算方法。方法采用EM算法对混合正态风险模型进行参数估计;采用Kolmogorov-Smirnov检验对混合正态风险模型的拟合优度进行检验;采用随机抽样模拟和t检验法比较随机样本指标与模型参数之间的差异;采用逐步判别分析方法,对随机保单进行分类与甄别;设计保险条款,作为保险双方有约束力的合同。结果由训练样本拟合得到四元混合正态模型;模型的拟合精度很高(P=0·99701);按μi+1·645σi可得到4种保险等级下的总保费;样本指标与模型参数之间的差异无统计学意义。结论本文设计的面向糖尿病住院病人的医疗保险,可根据投保人因糖尿病住院风险损失额划分成4种类型保单持有者,并由此厘定出4种不同等级的保险费,因而体现了高风险损失应承担高额保险费的保险原则,有利于投保人根据自身情况选择保单类别。

Objective To study on an actuarial method based on mix normal distributions model for medical insurance of inpatients with diabetes. Methods The parameters of model were estimated using EM arithmetic. Goodness of fit of the model waS tested using Kolmogorov Smirnov Test. Compare with the different between the random sample index and the model parameters using random sampling simulation and t- test method. The random policyholders were classified and discriminated using stepwise discriminant analysis, The insuring clauses were designed by way of a binding contract of the insuring both sides. Results Mix normal distribution model with four normal variables was fitted by the training sample. Fitting precision of the model was high （P = 0.99701 ）. Gross premiums of four kinds of policyholders were calculated according to. The difference between the ran dora sample index and the model parameters was not statistically significant. Conclusion The medical insurance facing to the inpatients with diabetes designed by the article were divided into four kinds of policyholders by the medical risk loss in hospital of four kinds of subscribers with diabetes, The different grades of premium determined materialized the insurance principle that high medical risk should pay high premium, so that favor subscribers to choose policy sort by their situation.