Case studies in multivariate-to-anything transforms for partially specified random vector generation

This paper considers methods for sampling from random vectors characterized by marginal distributions and a correlation matrix, rather than a full joint distribution. The paper begins by describing the normal-to-anything (NORTA) transform for sampling from such random vectors. Limitations of the NORTA transformation motivate the development of a more general framework for partially specified random vector generation, and several alternatives to NORTA are described. NORTA and its alternatives are compared to a previous methodology for generating bivariate gamma random vectors; while each method considered generates random vectors with gamma marginals and appropriate correlations, both NORTA and its alternatives are shown to offer what could be considered to be more desirable joint distributional qualities. Finally, it is demonstrated that in the context of generating multivariate gamma random vectors some of the limitations of NORTA can in fact be overcome by considering its alternatives.