Multivariate distribution derived from a Bernoulli mixed model under a marginal approach, incorporating a non-normal random intercept whose distribution is assumed to follow a generalized log-gamma (GLG) specification under a particular parameter setting. Estimation is performed by maximizing the log-likelihood using numerical optimization techniques (Lizandra C. Fabio, Vanessa Barros, Cristian Lobos, Jalmar M. F. Carrasco, Marginal multivariate approach: A novel strategy for handling correlated binary outcomes, 2025, under submission).