The University of Massachusetts Amherst
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Translation vectors with non-identically distributed components

TitleTranslation vectors with non-identically distributed components
Publication TypeJournal Article
Year of Publication2005
AuthorsArwade SR
JournalProbabilistic Engineering Mechanics
Start Page158
KeywordsCrystallographic orientation, Heterogeneous material properties, Non-Gaussian vectors, Non-stationary processes, Random processes, Random vectors, Translation vector

A model for non-Gaussian random vectors is presented that relies on a modification of the standard translation transformation which has previously been used to model stationary non-Gaussian processes and non-Gaussian random vectors with identically distributed components. The translation model has the ability to exactly match target marginal distributions and a broad variety of correlation matrices. Joint distributions of the new class of translation vectors are derived, as are upper and lower bounds on the target correlation that depend on the target marginal distributions. Examples are presented that demonstrate the applicability of the approach to the modeling of heterogeneous material properties, and also illustrate the possible shortcomings of using second moment characterizations for such random vectors. Lastly, an outline is given of a method under development for extending the model to non-stationary, non-Gaussian random processes.