Bivariate Simplex Distribution

Abstract: 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.