This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence between the variables and examine its relationship with the association parameter. Parameters are estimated using the maximum likelihood method, and their performance is assessed through Monte Carlo simulations. The simulations explore various aspects of the bivariate distribution, including different surfaces and contour graphs. To illustrate the proposed model's methodology and properties, we present an application in the Jurimetric area. A user-friendly package, BSimplex, is also available in the R software.

翻译：本文提出了一种用于建模约束在区间$(0,1)$内的连续结果（可表示比例、比率或指数）的二元Simplex分布。我们推导了计算变量间依赖关系的解析表达式，并考察了其与关联参数的关系。参数采用最大似然法进行估计，并通过蒙特卡洛模拟评估其性能。模拟研究了二元分布的不同方面，包括各种曲面和等高线图。为说明所提模型的方法与特性，我们展示了一个在司法计量学领域的应用案例。同时，在R软件中提供了一个用户友好的BSimplex程序包。