Comments on the Exchange between Hedges and Witt
评论赫奇斯与威特关于汽车保险公司损失率均值与标准差相关性的争论，指出威特用中心极限定理论证均值与方差无关的逻辑不成立。
The recent exchange between Hedges [1] and Witt [2] prompts a few additional comments. These are motivated by a concern for the misconceptions that might be created by those comments, not by a desire to take sides. Witt [3] had found a positive correlation between the temporal average of the loss ratio of automobile insurers in 51 jurisdictions and the standard deviation of the annual results from the temporal mean for each jurisdiction. The main issue in the exchange is whether one should view as surprising the fact that the correlation was positive. Hedges [1] proposes a mechanism which suggests to him that the correlation should be positive, and Witt [2] counters that the mathematical relation and institutional factors proposed by Hedges do not tend to make the correlation positive. The present comment addresses two issues: the relevance of the central limit theorem to the belief that the mean and standard deviation should be independent unless there are real, structural effects, and the relevance of the standard deviation as a measure of risk in the empirical study. Witt states: Mathematically, it can be shown that there is no relationship between the mean and variance of normally distributed random variables. Since the annual loss ratio of all the companies is nothing more than the weighted average loss ratio of all the companies writing a given coverage in a state, the Central Limit Theorem would suggest that the annual loss ratio in a state should be normally distributed. Therefore, it would seem quite reasonable to argue that there is no mathematical relationship between the mean and the variance of the annual loss ratios in a state. [2] This argument is not valid.