安徽省火灾经济损失的尾部分布研究

采用极大似然估计对安徽火灾经济损失进行了幂律分布拟合,采用Kolmogorov-Smirnov统计判断拟合优度,并选择了4种供选分布作为对比,研究何种分布更适用于描述火灾经济损失数据。研究发现,当经济损失大于100万元时,数据明显偏离幂律分布,通过p值可以拒绝数据服从幂律分布的假设。在5种分布中指数截断幂律分布的拟合效果最好,通过指数截断能够描述数据末端偏离幂律行为的现象。放火和生产作业两类原因的火灾,不仅满足幂律分布,而且指数截断幂律分布的拟合效果最优;不明确原因和静电两类原因的火灾,经济损失仅满足幂律分布;其他7种火灾原因对应的损失数据不能通过幂律分布拟合的p值检验。

Tail distribution of fire loss data in Anhui province

The power-law distribution of fire loss statistics in Anhui province was estimated by means of Maximum likelihood estimators. The goodness-of-fit test of power-law estimation was conducted in terms of Kolmogorov-Smirnov statistics. In order to judge whether it is possible another distribution might give a good or better fit, four alternative distributions were chosen and analyzed. According to results, the data significantly diverges from power-law distribution when the loss is over thousand Yuan. As the p-value of goodness-of-fit is zero, the power-law distribution is not a plausible hypothesis for the data. The power-law with an exponential cutoff is clearly favored over the other four distributions, and it can depict the deviation from power-law distribution in the end of loss. For fires caused by arson and working, their loss data pass the p-value of goodness-of-fit test, and the power-law with an exponential cutoff is more favored than the power-law distributions. For fires caused by unknown and electrostatic, their loss data pass the p-value of goodness-of-fit test as well, and power-law is the best fitting. For fires caused by the other 7 causes, their loss data cannot pass the p-value of goodness-of-fit test.