Abstract

In this paper, we make use of meta-elliptical copula functions to build a new multivariate distribution with fixed marginal distributions and dependence structure to analyze bounded data. Specifically, we present a flexible p-elliptical multivariate probability distribution in the hypercube ${(0,1)}^p$ p with fixed marginal GF-quantile distributions. We then present some illustrative examples and a meta-elliptical multivariate regression model as a flexible alternative to the multivariate normal regression model on unit intervals. A simulation study and real-life data analysis using a Bayesian framework with the extreme-value quantile functions show the flexibility of the proposed meta-multivariate normal regression model for modeling the observed proportion response variables.

摘要

在本文中，我们利用元椭圆 copula 函数构建具有固定边际分布和依赖结构的新多元分布来分析有界数据。具体来说，我们在超立方体中提出了一个灵活的 p-椭圆多元概率分布${(0,\mathrm{1个})}^p$p 具有固定的边际 GF 分位数分布。然后，我们提供了一些说明性示例和元椭圆多元回归模型，作为单位间隔上多元正态回归模型的灵活替代方案。使用具有极值分位数函数的贝叶斯框架进行的模拟研究和现实生活中的数据分析显示了所提出的元多元正态回归模型对观察到的比例响应变量建模的灵活性。