What distribution function do life cycle inventories follow?

  • Yuwei Qin
  • Sangwon Suh



Life cycle inventory (LCI) results are often assumed to follow a lognormal distribution, while a systematic study that identifies the distribution function that best describes LCIs has been lacking. This paper aims to find the distribution function that best describes LCIs using Ecoinvent v3.1 database using a statistical approach, called overlapping coefficient analysis.


Monte Carlo simulation is applied to characterize the distribution of aggregate LCIs. One thousand times of simulated LCI results are generated based on the unit process-level parametric uncertainty information, from each of which 1000 randomly chosen data points are extracted. The 1 million data points extracted undergo statistical analyses including Shapiro-Wilk normality test and the overlapping coefficient analysis. The overlapping coefficient is a measure used to determine the shared area between the distribution of the simulated LCI results and three possible distribution functions that can potentially be used to describe them including lognormal, gamma, and Weibull distributions.

Results and discussion

Shapiro-Wilk normality test for 1000 samples shows that average p value of log-transformed LCI results is 0.18 at 95 % confidence level, accepting the null hypothesis that LCI results are lognormally distributed. The overlapping coefficient analysis shows that lognormal distribution best describes the distribution of LCI results. The average of overlapping coefficient (OVL) for lognormal distribution is 95 %, while that for gamma and Weibull distributions are 92 and 86 %, respectively.


This study represents the first attempt to calculate the stochastic distributions of the aggregate LCIs covering the entire Ecoinvent 3.1 database. This study empirically shows that LCIs of Ecoinvent 3.1 database indeed follow a lognormal distribution. This finding can facilitate more efficient storage and use of uncertainty information in LCIs and can reduce the demand for computational power to run Monte Carlo simulation, which currently relies on unit process-level uncertainty data.


Ecoinvent 3.1 Life cycle inventory Lognormal distribution Monte Carlo simulation Probability distribution Uncertainty analysis 



We are thankful to Guillaume Bourgault, Ecoinvent Project Manager, for providing data and assisting us to better understanding the database. His help and support is invaluable to the research. This publication was developed under Assistance Agreement No. 83557901 awarded by the U.S. Environmental Protection Agency to University of California Santa Barbara. It has not been formally reviewed by EPA. The views expressed in this document are solely those of the authors and do not necessarily reflect those of the Agency. EPA does not endorse any products or commercial services mentioned in this publication.

Supplementary material

11367_2016_1224_MOESM1_ESM.docx (120 kb)
ESM 1 The results of lognormal distributions of 1000 LCIs are presented in the supporting material. Also provided in the supporting information are the QQ-plot of nine random log-transformed LCI results and mathematical notations for five distribution types that are relevant to our study. (DOCX 119 kb)
11367_2016_1224_MOESM2_ESM.xlsx (102 kb)
ESM 2 (XLSX 102 kb)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Bren School of Environmental Science and ManagementUniversity of CaliforniaSanta BarbaraUSA

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