Hessian orderings of multivariate normal variance-mean mixture distributions and their applications in evaluating dependent multivariate risk portfolios

2021 ◽  
Author(s):  
Mehdi Amiri ◽  
Narayanaswamy Balakrishnan ◽  
Abbas Eftekharian
Keyword(s):  
Mixture Distributions ◽  
Multivariate Normal ◽  
Multivariate Risk ◽  
Normal Variance

Uncertainty Modeling Using Mixture Distributions in Engineering Systems

2017 ◽  
Author(s):  
Vijitashwa Pandey ◽  
Zissimos P. Mourelatos ◽  
Judson Estes
Keyword(s):  
Maximum Likelihood ◽  
Uncertainty Modeling ◽  
Mixture Distributions ◽  
Engineering Systems ◽  
Limited Information ◽  
Multivariate Normal ◽  
Limited Data ◽  
Normal Distributions ◽  
Efficient Calculation ◽  
Application Problem

Uncertainty is an engineering reality. Attempts to model and reconcile with this uncertainty are generally thwarted by the dearth of available data. In this paper, we use the concept of mixture distributions to address uncertainty modeling under limited information. Mixtures allow for flexibility in modeling of the distributions in question, especially when multimodality exists, is expected to exist, or the data does not come from any of the well-known distributions types. This is expected and observed in domains such as manufacturing, where data intrinsically comes from various sources — e.g. a part provided by multiple suppliers. The proposed approach uses a maximum likelihood based optimization algorithm (EM algorithm) to model limited data as a mixture of multivariate normal distributions. The application problem we choose is that of alignment of vehicles during manufacture. For the application problem, our approach is able to accurately predict repair frequency and outperforms the use of a single multivariate distribution. Our results indicate that the use of mixture distributions warrants further investigations particularly for efficient calculation of expectations of metrics of interest in engineering design.

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