An approximate-copula distribution for statistical modeling

Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three frameworks. Based on prior work of Tonda, we derive a new class of probability density functions that allow explicit calculation of moments, marginal and conditional distributions, and the score and observed information needed in maximum likelihood estimation. We also illustrate how the new distribution flexibly models longitudinal data following a non-Gaussian distribution. Finally, we conduct a tri-variate genome-wide association analysis on dichotomized systolic and diastolic blood pressure and body mass index data from the UK-Biobank, showcasing the modeling potential and computational scalability of the new distributional family.