『Abstract
　The Hubbert theory of oil depletion, which states that oil production in large regions follows a bell-shaped curve over time, has been cited as a method to predict the future of global oil production. However, the assumptions of the Hubbert method have never been rigorously tested with a large, publicly available data set. In this paper, three assumptions of the modern Hubbert theory are tested using data from 139 oil producing regions. These regions are sub-national (United States state-level, United States regional-level), national, and multi-national (subcontinental and continental) in scale. We test the assumption that oil production follows a bell-shaped curve by generating best-fitting curves for each region using six models and comparing the quality of fit across models. We also test the assumption that production over time in a region tends to be symmetric, and that production is more bell-shaped in larger regions than in smaller regions.

Keywords: Petroleum; Hubbert theory; Oil depletion』

1. Introduction and context
　1.1. The hubbert theory of oil depletion
　1.2. Alternative models of oil depletion
　1.3. Problems with current depletion analysis
2. Methods of analysis
　2.1. Data sets used
　2.2. Methodology to determine best fitting model in each region
　　2.2.1. Comparing models
　　　2.2.1.1. Three-model comparison (comparing only symmetric models)
　　　2.2.1.2. Six-model comparison (symmetric and 　asymmetric models)
　2.3. Methodology to test the symmetry of regional oil production
　2.4. Methodology to test the quality of the Hubbert fit across regions of different sizes
3. Results
　3.1. Best-fitting model results
　　3.1.1. Three-model comparison: best fit between symmetric models
　　3.1.2. Six-model comparison: best fit between all models
　3.2. Symmetry of regional oil production
　3.3. Hubbert fit across regions of different size
4. Discussion and conclusion
Acknowledgments
Appendix A. Definition of regions
Appendix B. Mathematical formulation of six tested models
　B.1. Symmetric models
　　B.1.1. Hubbert
　　B.1.2. Linear
　　B.1.3. Exponential
　B.2. Asymmetric models
　　B.2.1. Asymmetric Hubbert
　　B.2.2. Asymmetric linear
　　B.2.3. Asymmetric exponential
References