The mixture approach is an exact methodology for simulating new families of bivariate distributions with specified correlation coefficients. It accommodates the entire range of correlations, produces bivariate surfaces that are intuitively appealing, and is often remarkably easy to implement. The approach is introduced in a Bayesian context and demonstrated for the conjugate families of beta an...

The association between two ordinal variables can be expressed with a polychoric correlation coefficient. This coefficient is conventionally based on the assumption that responses to are generated by underlying continuous latent bivariate normal distribution. When normality violated, estimated may biased. In such case, we consider other distributions. this paper, aimed provide an illustration o...