Statistical simulation based on right skewed distributions

Statistical simulations in medical and biological research are usually conducted with normal random numbers. However, in many cases, the distributions of real data in medical fields are usually right skewed. The conclusions led by simulations with the misspecified model might be misleading because of a gap between real data’s distribution and theoretical one. In this paper, we provide the simulation procedure for right skewed data based on reparameterized, easily interpretable parameters of the Box–Cox transformation model which includes multivariate distributions and regression models. We also show that the provided procedure is widely applicable to real world based on laboratory data, and then we provide parameter vector sets obtained by reparameterized parameter estimates that would cover almost all situations in which the distributions of data were right skewed and unimodal.