On the Distribution of Crop Yields: Does the Central Limit Theorem Apply?
研究了中心极限定理是否适用于加总作物产量，发现当作物种植面积随时间大幅波动时，加总产量可能不服从正态分布，并用美国州级作物产量数据验证了这一假设。
In this article, we investigate the applicability of the central limit theorem (CLT) to aggregate crop yields. We argue that the aggregation of elementary crop yields is likely to produce nonnormal distributions if, contrary to the standard CLT case, the number of crop acres exhibits substantial time variation. This case is covered by limit theorems for random sums of random variables, which predict nonnormal limiting distributions. The case of substantial variation in the number of summands produces an empirical hypothesis that we test using data from U.S. aggregate state crop yields. The results provide empirical support against the applicability of the CLT.