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 prowess and computational scalability of the new distribution.

翻译：Copula、广义估计方程和广义线性混合模型促进了组内相关非正态响应数据的分析。然而，在这三种框架中，参数估计仍然具有挑战性。基于Tonda的前期工作，我们推导出一类新的概率密度函数，该类函数允许显式计算矩、边缘与条件分布，以及最大似然估计中所需的得分函数和观测信息。我们还展示了新分布如何灵活地对服从非高斯分布的纵向数据进行建模。最后，我们对来自UK-Biobank的二值化收缩压、舒张压和体重指数数据进行了三变量全基因组关联分析，展示了新分布的建模能力和计算可扩展性。