The Weight of Euro Coins: Its Distribution Might Not Be As Normal As You Would Expect
The Weight of Euro Coins: Its Distribution Might Not Be As Normal As You Would Expect
复制标题
欧元硬币的重量：它的分布可能不像你想象的那么正常
DOI：
10.1080/10691898.2006.11910585
复制
发表时间：
2006
影响因子：
2.2
通讯作者：
H. Callaert
中科院分区：
文献类型：
--
作者：
Z. Shkedy;M. Aerts;H. Callaert
经典回归模型、ANOVA模型和线性混合模型只是响应的正态分布是模型基本假设的三个例子。在本文中，我们使用的数据集包含2000欧元硬币的信息（高达毫克），每个硬币的重量，以说明正态假设可能是不正确的。由于实物硬币的生产过程受到多种（非常小的）可变性来源的影响，因此可以合理地预期欧元硬币重量的经验分布确实符合正态分布。然而，拟合优度检验表明，情况并非如此。此外，一些离群值使分析复杂化。作为替代方法，正态分布和偏正态分布的混合物被拟合到数据中，并揭示了欧元硬币重量的分布并不像预期的那样正态。
Classical regression models, ANOVA models and linear mixed models are just three examples (out of many) in which the normal distribution of the response is an essential assumption of the model. In this paper we use a dataset of 2000 euro coins containing information (up to the milligram) about the weight of each coin, to illustrate that the normality assumption might be incorrect. As the physical coin production process is subject to a multitude of (very small) variability sources, it seems reasonable to expect that the empirical distribution of the weight of euro coins does agree with the normal distribution. Goodness of fit tests however show that this is not the case. Moreover, some outliers complicate the analysis. As alternative approaches, mixtures of normal distributions and skew normal distributions are fitted to the data and reveal that the distribution of the weight of euro coins is not as normal as expected.