Vasicek Quantile and Mean Regression Models for Bounded Data: New Formulation, Mathematical Derivations, and Numerical Applications

The Vasicek distribution is a two-parameter probability model with bounded support on the open unit interval. This allows for different and flexible shapes plays an important role in many statistical applications, especially modeling default rates field of finance. Although its density function resembles some well-known distributions, such as beta Kumaraswamy models, has not been considered to analyze data interval, when we have, addition response variable, one or more covariates. In this paper, propose estimate quantiles means, conditional covariates, assuming that variable distributed. Through appropriate link functions, two regression models interval are formulated: considers quantile parameterization another original parameterization. Monte Carlo simulations provided assess properties maximum likelihood estimators, well coverage probability. An R package developed by authors, named vasicekreg, makes available results present investigation. Applications real sets conducted illustrative purposes: them, outperforms based Johnson-SB, Kumaraswamy, unit-logistic, unit-Weibull whereas second one, mean fits obtained simplex distributions. Our investigation suggests regressions can be practical usage alternatives analyzing