《准备金评估的GL》PPT课件

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1、准备金评估的GLM孟生旺中国人民大学统计学院http://blog.sina.com.cn/mengshw1GLM模型的结构分布假设线性预测项连接函数2GLM模型的检验和比较关于解释变量：是否显著？方差分析，P值是否分段？是否线性？平滑函数是否存在交互效应？关于分布假设：残差分析：QQ图，蠕虫图。流量三角形的数据有限，分布假设的影响显著关于连接函数？模型比较：AIC=-2l+2*参数个数3准备金评估的数据格式流量三角形数据框4事故年进展年123456789101357,848766,940610,542482,940527,32657

2、4,398146,342139,950227,22967,9482352,118884,021933,8941,183,289445,745320,996527,804266,172425,0463290,5071,001,799926,2191,016,654750,816146,923495,992280,4054310,6081,108,250776,1891,562,400272,482352,053206,2865443,160693,190991,983769,488504,851470,6396396,132937,08

3、5847,498805,037705,9607440,832847,6311,131,3981,063,2698359,4801,061,6481,443,3709376,686986,60810344,014增量赔款的流量三角形格式（Taylor，1983）5增量赔款的数据框格式事故年进展年增量赔款11357848127669401361054214482940155273261657439817146342181399501922722911067948213521182288402123933894241183289254457

4、452632099627527804282661722942504631290507………6描述性统计分析78910第1个事故年的进展趋势比较特殊？11均值和方差方差=122188299213方差/均值=195597Min.1stQu.MedianMean3rdQu.Max.67950352100527300624700905100156200012泊松分布拟合：图中泊松分布的概率被缩小为实际值的1%1314伽马分布拟合描述性分析的初步结论增量赔款右偏，方差远远大于均值，伽马拟合较好第1个事故年的进展模式与其它事故年不同15建模分布假

5、设：泊松（链梯法）伽马解释变量：事故年、进展年、日历年形式：离散、连续连接函数：对数16泊松回归增量赔款~泊松分布log(增量赔款)=事故年+进展年1712345678910准备金13578481,124,7881,735,3302,218,2702,745,5963,319,9943,466,3363,606,2863,833,5153,901,46323521181,236,1392,170,0333,353,3223,799,0674,120,0634,647,8674,914,0395,339,0855,433,71994,6

6、3432905071,292,3062,218,5253,235,1793,985,9954,132,9184,628,9104,909,3155,378,826469,51143106081,418,8582,195,0473,757,4474,029,9294,381,9824,588,2685,297,906709,63854431601,136,3502,128,3332,897,8213,402,6723,873,3114,858,200984,88963961321,333,2172,180,7152,985,7523,6

7、91,7125,111,1711,419,45974408321,288,4632,419,8613,483,1305,660,7712,177,64183594801,421,1282,864,4986,784,7993,920,30193766861,363,2945,642,2664,278,972103440144,969,8254,625,811进展因子3.49060651.7473331.4574131.1738521.1038241.0862691.0538741.0765551.01772473累积进展因子14.446

8、5774.1387012.3685821.6251961.3844991.2542761.1546641.0956371.01772473准备金合计18,680,856链梯法（使用累积赔款数据）18泊松回归的结果注意：泊