Giesbrecht F G, Whitaker T B
Department of Statistics, North Carolina State University, Raleigh 27695-8203, USA.
Biometrics. 1998 Jun;54(2):739-53.
In this study, a number of probability distributions that have been used to model the occurrence of aflatoxin in peanuts are compared. Two distributions, the compound gamma and the negative binomial, are shown to have special appeal in that both can be justified by reasoning from the fundamental biological and stochastic processes that generate the aflatoxin. Since method of moments and maximum likelihood give consistent estimates of parameters in both models, practical considerations suggest using the former. One hundred twenty data sets, each consisting of fifty observations, were not sufficient to provide goodness-of-fit tests to establish either as superior to the other as a model. Both models fit the data well, appreciably better than other models examined. An attractive aspect of the compound gamma and the negative binomial distributions is that, as a consequence of their theoretical underpinnings, both involve parameters that have meaningful interpretations. In the compound gamma, the alpha parameter reflects the shape of the kernel-to-kernel aflatoxin content distribution, the lambda parameter reflects the number (or frequency) of contaminated kernels in the sample, and the beta parameter is a scale parameter. In the negative binomial, the two parameters can be used as measures of mean or location and shape.
在本研究中，对一些用于模拟花生中黄曲霉毒素发生情况的概率分布进行了比较。复合伽马分布和负二项分布这两种分布具有特殊的吸引力，因为它们都可以通过对产生黄曲霉毒素的基本生物学和随机过程进行推理来证明其合理性。由于矩估计法和最大似然估计法在这两种模型中都能给出一致的参数估计值，从实际考虑出发建议使用前者。120个数据集，每个数据集由50个观测值组成，不足以提供拟合优度检验来确定其中一个模型优于另一个模型。这两种模型对数据的拟合都很好，明显优于所检验的其他模型。复合伽马分布和负二项分布的一个吸引人的方面是，由于它们的理论基础，两者都涉及具有有意义解释的参数。在复合伽马分布中，α参数反映了粒间黄曲霉毒素含量分布的形状，λ参数反映了样本中受污染籽粒的数量（或频率），β参数是一个尺度参数。在负二项分布中，这两个参数可以用作均值或位置以及形状的度量。
