Beyond ‘lognormal versus gamma’: discrimination among error distributions for generalized linear models

The process of model selection includes making an assumption about the distribution of ‘errors’ about the mean response. Generalized linear models (GLMs) offer considerable flexibility in this regard. However, graphical methods for identifying potential error distributions can fail to discriminate among sets of candidate error distributions. I examine an information-theoretic approach to this issue, which ranks candidate models (error distributions) using Akaike's information criterion (AIC). I evaluate the effectiveness of this technique using Monte Carlo simulation by generating pseudorandom data from five skewed distributions: lognormal, gamma, Weibull, log-logistic, and inverse Gaussian. I then fit each data set under all five distributional assumptions, and examine how well AIC identifies the distribution that generated the data. On the basis of the simulations, I suggest that AIC is effective at identifying the data-generating distribution, given moderate to large sample sizes. I then fit four candidate models to data drawn from a mixture of four distributions with common expectations and coefficients of variation (CVs). AIC did not show strong support for a particular candidate model given small samples of ‘mixed’ data, although larger samples selected the gamma distribution for CVs of 0.5 and 1.0, and the Weibull distribution for CVs of 1.5 and 2.0. Finally, I apply this technique in a GLM setting to several fisheries-independent and -dependent data sets to select the error distribution that is best supported by the data. Twenty-one out of 24 fisheries data sets examined showed strong support for one of the five candidate error distributions and the remaining moderate support for two.     

枣庄市主要树种直径结构比较研究

分析了枣庄市市中区3种主要树种黑杨、刺槐和侧柏的直径结构特征,运用5种分布函数正态分布、Weibull分布、对数正态分布、Gamma分布以及logistic分布对这3种树的林分的直径分布进行了拟合,同时用卡方统计量对5种分布进行了检验,拟合和检验得出了一致的结果。     

不同栽培模式下冬小麦根系直径的频率分布

为明确不同栽培模式下冬小麦根系生长情况,以矮抗58为材料,通过分析高产、高效和高产高效三种栽培模式下冬小麦根系直径频率所服从的对数正态分布的参数μ和σ,探讨了根系的拓扑结构。结果表明,3种模式下,0~20cm和20~40cm土层中小麦根系在特定时期内都表现出能高效运输营养物质的鲱鱼骨形结构,但根系调整为鲱鱼骨形结构的时期和出现位置存在差异。高效模式下,根系鲱鱼骨形结构于拔节前和灌浆前在两个土层中都有出现;高产高效模式下,根系鲱鱼骨形结构于拔节前在两个土层中出现,灌浆前只在0~20cm土层出现,而20~40cm土层根系出现鲱鱼骨形结构则是在灌浆中后期;高产模式下,根系鲱鱼骨形结构于拔节前出现在0~20cm土层,拔节期两个土层中均出现,而灌浆中后期则只出现在20~40cm土层。从根系结构来看,高产高效模式下,小麦根系可以间接限制营养生长,且在灌浆中后期可以利用深层土壤的营养物质,是具有潜力的栽培模式。     

枣庄市黑杨直径结构的模拟研究

分析了黑杨树的直径结构特征,分别利用5种分布函数即正态分布、Weibull分布、Gamma分布、对数正态分布以及Logistic分布对黑杨树林的直径分布进行了拟合,同时用卡方统计量对5种分布进行了检验。拟合结果和检验结果一致表明,在这5个拟合分布函数中,Weibull分布用于拟合黑杨树林分直径分布的效果最好,Gamma分布的拟合效果次之。