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Quantification of Variability and Uncertainty Using Mixture Distributions: Evaluation of Sample Size, Mixing Weights, and Separation Between Components

机译：使用混合物分布对变异性和不确定性进行定量：评估样品大小，混合权重和组分之间的分离

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摘要

Variability is the heterogeneity of values within a population. Uncertainty refers to lack of knowledge regarding the true value of a quantity. Mixture distributions have the potential to improve the goodness of fit to data sets not adequately described by a single parametric distribution. Uncertainty due to random sampling error in statistics of interests can be estimated based upon bootstrap simulation. In order to evaluate the robustness of using mixture distribution as a basis for estimating both variability and uncertainty, 108 synthetic data sets generated from selected population mixture log-normal distributions were investigated, and properties of variability and uncertainty estimates were evaluated with respect to variation in sample size, mixing weight, and separation between components of mixtures. Furthermore, mixture distributions were compared with single-component distributions. Findings include: (1) mixing weight influences the stability of variability and uncertainty estimates; (2) bootstrap simulation results tend to be more stable for larger sample sizes; (3) when two components are well separated, the stability of bootstrap simulation is improved; however, a larger degree of uncertainty arises regarding the percentiles coinciding with the separated region; (4) when two components are not well separated, a single distribution may often be a better choice because it has fewer parameters and better numerical stability; and (5) dependencies exist in sampling distributions of parameters of mixtures and are influenced by the amount of separation between the components. An emission factor case study based upon NO_x emissions from coal-fired tangential boilers is used to illustrate the application of the approach.
机译：变异性是总体中价值的异质性。不确定性是指对数量的真实价值缺乏了解。混合物分布有可能提高对单一参数分布未充分描述的数据集的拟合优度。可以基于自举仿真来估计由于兴趣统计中的随机采样误差导致的不确定性。为了评估使用混合分布作为估计变异性和不确定性的基础的鲁棒性，研究了从选定总体混合对数正态分布中生成的108个综合数据集，并对变异性和不确定性估计的特性进行了评估。样品大小，混合重量以及混合物组分之间的分离。此外，将混合物分布与单组分分布进行了比较。研究结果包括：（1）混合权重影响可变性和不确定性估计的稳定性； （2）对于较大的样本量，引导程序仿真结果倾向于更稳定； （3）当两个组件很好地分开时，引导仿真的稳定性得到提高；但是，与分隔区域一致的百分位数会产生较大程度的不确定性； （4）当两个成分没有很好地分离时，由于分布参数少，数值稳定性更好，所以通常最好选择单一分布。 （5）混合物参数的采样分布中存在依存关系，并受组分之间的分离量影响。基于燃煤切线锅炉NO_x排放的排放因子案例研究用于说明该方法的应用。

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