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Random Variable Estimation and Model Calibration in the Presence of Epistemic and Aleatory Uncertainties

Journal Article
ISSN: 1946-3979, e-ISSN: 1946-3987
Published April 03, 2018 by SAE International in United States
Random Variable Estimation and Model Calibration in the Presence of Epistemic and Aleatory Uncertainties
Citation: Gaymann, A., Pietropaoli, M., Crespo, L., Kenny, S. et al., "Random Variable Estimation and Model Calibration in the Presence of Epistemic and Aleatory Uncertainties," SAE Int. J. Mater. Manf. 11(4):453-466, 2018,
Language: English


  1. Glickman, M. Schroeder, B. and Romero, V. , “Cantilever Beam End-to-End UQ Test Problem: Handling Experimental and Simulation Uncertainties in Model Calibration, Model Validation, and Risk Assessment, Sandia National Laboratories,” SAND2017-4689 O, 2017.
  2. Helton, J.C., Oberkampf, W. et al. , “Challenge Problems: Uncertainty in System Response Given Uncertain Parameters,” Reliability Engineering and System Safety 85:11-19, 2004.
  3. Roy, C. and Oberkampf, W. , “A Comprehensive Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing,” Computer Methods in Applied Mechanics and Engineering 200(2011):2131-2144, 2004.
  4. Nakos, J.T. , “Uncertainty Analysis of Thermocouple Measurements Used in Normal and Abnormal Thermal Environment Experiments at Sandia Radiant Heat Facility and Lurance Canyon Burn Site,” Sandia National Labs., SAND2004-1023, Apr. 2004.
  5. Hosking, J.R.M. and Wallis, J.R. , “Guide to the Evaluation of Measurement Uncertainty for Quantitative Test Results,” EUROLAB, Paris, France, Aug. 2006, 8, Retrieved Mar. 2, 2017.
  6. Chakraborti, S. and Dickinson Gibbons, J. , Nonparametric Statistical Inference, Fifth Edition, STATISTICS: Textbooks and Monographs (Chapman and Hall/CRC Press, 2010), ISBN:9781420077612.
  7. Kraaikamp, C., Dekkling, F.M. et al. , A Modern Introduction to Probability and Statistics, Springer Texts in Statistics (2005).
  8. Wolfowitz, J., Dvoretzky, A., and Kiefer, J. , “Asymptotic Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator,” The Annals of Mathematical Statistics 27(3):642-669, 1956.
  9. Massart, P. , “The Tight Constant in the Dvoretzky-Kiefer-Wolfowitz Inequality,” The Annals of Probability, 1990.
  10. Scholz, F.W. , “Nonparametric Tail Extrapolation,” Technical Report, ISSTECH-95-014, Boeing Information & Support Services, 1995.
  11. Donald, A.M. and Scarrott, C. , “Review of Extreme Value Threshold Estimation and Uncertainty Quantification,” Statistical Journal 10(1):33-60, 2012.
  12. Rutledge, J. and Warner, B.A. , “Simple Nonparametric Upper and Lower Tolerance Bounds Based on Order Statistics,” USAFA/DFMS, n.d.
  13. Learned-Miller, E. and DeStefano, J. , “A Probabilistic Upper Bound on Differential Entropy,” IEEE Transactions on Information Theory, 2008.
  14. Natarajan, K., Betrsimas, D. et al. , “Tight Bounds on Expected Order Statistics,” Probability in the Engineering and Information Sciences, 2006.
  15. Hosking, J.R.M. and Wallis, J.R. , “Parameter and Quantile Estimation for the Generalized Pareto Distribution,” Technometrics 29(3):339-349, 1987.
  16. Dufour, J.M. and Diouf, M.A. , “Improved Nonparametric Inference for the Mean of a Bounded Random Variable with Application to Poverty Measures,” Working Paper, Departement de Sciences Economiques, Universite de Montreal, May 2005.
  17. Lezaud, P. and Charras-Garrido, M. , “Extreme Value Analysis: An Introduction,” Journal de la Societe Francaise de Statistique, 2013.
  18. Tawn, J.A. and Papastathopoulos, I. , “Extended Generalized Pareto Models for Tail Estimation,” Journal of Statistical Planning and Inference 143:131-143, 2013.
  19. Anderson, T.W. , “Confidence Limits for the Value of an Arbitrary Bounded Random Variable with a Continuous Distribution Function,” Bulletin of the International and Statistical Institute, 1969.
  20. Wolf, M. and Romano, J.P. , “Explicit Nonparametric Confidence Intervals for the Variance with Guaranteed Coverage,” Communications in Statistics - Theory and Methods, 2002.
  21. Reynolds, D.A. , “Gaussian Mixture Models,” in: Encyclopedia of Biometrics (2009).
  22. Clifton, L., Clifton, D.A. et al. , “Extending the Generalized Pareto Distribution for Novelty Detection in High-Dimensional Spaces,” Journal of Signal Processing Systems 2014 74(3):323-339, Aug. 2013.

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