Simulation of multivariate gamma data with exponential marginals for independent clusters

Abstract

The theory of simulating multivariate gamma data with exponential marginals is presented, using multivariate normal data to generate a Wishart matrix, and then extracting the multivariate gamma vector. Only the correlation structure of the multivariate normal data must be specified in order to generate a multivariate gamma vector with the desired mean and variance ‐ covariance structure. A vector of such data is generated for a single group, and then for multiple, independent groups that may or may not be identically distributed. This method simulates positively correlated data due the fact that the correlation is a function of variance components. An example for failure time data in survival analysis is presented, including censoring and discrete covariates, and where each independent vector of multivariate gamma data has an exchangeable correlation structure

Keywords:

• correlation
• exchangeable correlation structure
• survival analysis
• multivariate exponential