Effect of Normal Transformation Methods on Performance of Multivariate Normal Distribution
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 8, Issue 1
Abstract
Multivariate normal distribution is used widely to characterize the uncertainties and correlations for correlated geotechnical data. The success of constructing a multivariate normal distribution depends on the reliable estimation of the marginal probability density functions (PDFs) and the correlation matrix. This paper focused on the normal transformation which is related to the fitted marginal PDFs and investigated its effect on the performance of the constructed multivariate normal distributions, i.e., the normality of the multivariate normal distribution, the fitness of the simulated data with the original data, the rationality of the derived point estimate equations, and validation of the equations based on validation data sets. Three normal transformation methods with different types of fitted marginal PDF, namely Johnson transformation, three-parameter lognormal transformation, and Box–Cox transformation, were compared based on their application to a real soil database. It was found that all the three normal transformation methods are applicable in the framework of multivariate normal distribution, although the transformed variables do not follow the multivariate normal distribution. The consistence of normality of the transformed variables with the performance of the constructed multivariate normal distribution in estimating the unknown parameters using Bayesian updating technique was verified. The Johnson transformation method is the recommended method for constructing the multivariate normal distribution for the real databases due to its robustness and superiority in normal transformation.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This study is substantially supported by the Natural Science Foundation Committee Program (No. 52022070) and by the Shanghai Municipal Science and Technology Committee Program (20dz1202200). The authors are grateful to these programs.
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ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 8 • Issue 1 • March 2022
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© 2021 American Society of Civil Engineers.
History
Received: May 30, 2021
Accepted: Sep 8, 2021
Published online: Oct 21, 2021
Published in print: Mar 1, 2022
Discussion open until: Mar 21, 2022
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