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Uncertainty Assessment of Non-normal Emission Estimates Using Non-parametric Bootstrap Confidence Intervals

L. I. Tong*, R. Saminathan1* and C. W. Chang

    Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu 300, Taiwan

*Corresponding author. Tel: +91-9944382772 Fax: +886-3-5731896 Email:


Mitigating global warming problems initially involves reducing greenhouse gas (GHG) emissions, therefore the uncertainty of GHG emission estimates needs to be assessed concisely. Although the uncertainty of GHG emission estimates is generally evaluated using classical confidence interval, quantifying the uncertainty based on non-normal GHG emission estimates or small dataset may lead to a significant bias. Using bootstrap confidence intervals is an effective means of reducing such a bias. This study presents a procedure for constructing four bootstrap confidence intervals to assess the uncertainty of GHG emission estimates for three non-normal distributions (namely, Weibull, Gamma and Beta). These bootstrap confidence intervals are standard bootstrap (SB) conï¬dence interval, percentile bootstrap (PB) conï¬dence interval, Bias-corrected percentiles bootstrap (BCPB) conï¬dence interval and bias-corrected and accelerated (BCa) conï¬dence interval. The sensitivity of bootstrap intervals for emission data is examined under various combinations of sample size and parameters of underlying non-normal distributions using three indices: coverage performance, interval mean, and interval standard deviation. Simulation results indicate that the bootstrap confidence intervals for assessing the uncertainty of emission estimates are highly applicable with small sample size and the data distribution is non-normal. Compared with the classical confidence interval, bootstrap confidence intervals have smaller interval mean and smaller interval standard deviation for small sample size under non-normal distributions. This study recommends BCa confidence interval to assess the uncertainty of the emission estimates as long as sample size is 15 or more and the distribution is non-normal. A case study with emission data of the High-Bleed Pneumatic controllers demonstrates the effectiveness of the proposed procedure.

Keywords: bootstrap confidence intervals, greenhouse gases, emissions, non-normal distributions, uncertainties

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