| 摘要: |
| 本文研究了Erlang混合分布和广义帕累托分布混合模型的估计问题.通过引入iSCAD惩罚函数,利用EM算法极大化iSCAD惩罚似然函数的方法,获得了混合序和参数的估计值,计算出有效的度量风险指标value-at-risk(VaR)和tail-VaR(TVaR),通过模拟实验和实际数据说明了模型和算法的有效性.推广了有限Erlang极值混合模型在保险数据拟合中的应用. |
| 关键词: 极值理论 极值混合模型 iSCAD惩罚 EM算法 似然函数 |
| DOI： |
| 分类号:O212.1 |
| 基金项目:国家自然科学基金资助(11201352). |
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| EFFICIENT ESTIMATION OF ERLANG AND GPD MIXTURES USING ISCAD PENALTY WITH INSURANCE APPLICATION |
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YIN Cui-hong1, LIN Xiao-dong1,2, YUAN Hai-li3
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1.School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;2.Department of Statistical Sciences, University of Toronto, Ontario M5S 3G3, Canada;3.School of Mathematics and Statistics Sciences, Wuhan University, Wuhan 430072, China
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| Abstract: |
| In this paper, we study efficient estimation of Erlang & GPD mixture model. By using a new thresholding penalty function and a corresponding EM algorithm, we estimate model parameters and determine the order of the mixture model. We obtain risk measure including VaR and TVaR and show efficiency of the new mixture model in simulation studies and a real data application, which improve Erlang & extreme value mixture model in modeling insurance losses. |
| Key words: extreme value theory mixture model iSCAD penalty EM algorithm likelihood function |
