The Box-Cox symmetric distributions constitute a broad class of probability models for positive continuous data, offering flexibility in modeling skewness and tail behavior. Their parameterization allows a straightforward quantile-based interpretation, which is particularly useful in regression modeling. Despite their potential, only a few specific distributions within this class have been explored in regression contexts, and zero-adjusted extensions have not yet been formally addressed in the literature. This paper formalizes the class of Box-Cox symmetric regression models and introduces a new zero-adjusted extension suitable for modeling data with a non-negligible proportion of observations equal to zero. We discuss maximum likelihood estimation, assess finite-sample performance through simulations, and develop diagnostic tools including residual analysis, local influence measures, and goodness-of-fit statistics. An empirical application on basic education expenditure illustrates the models' ability to capture complex patterns in zero-inflated and highly skewed nonnegative data. To support practical use, we developed the new BCSreg R package, which implements all proposed methods.

翻译：Box-Cox对称分布构成了一个广泛的概率模型类，适用于正连续数据，在建模偏态和尾部行为方面具有灵活性。其参数化允许基于分位数的直观解释，这在回归建模中尤为有用。尽管具有潜力，该类别中仅有少数特定分布在回归情境中得到探索，且零调整扩展在文献中尚未得到正式讨论。本文形式化了Box-Cox对称回归模型类，并引入了一种适用于具有不可忽略零值观测比例数据建模的新零调整扩展。我们讨论了最大似然估计，通过模拟评估有限样本性能，并开发了包括残差分析、局部影响度量和拟合优度统计在内的诊断工具。一项关于基础教育支出的实证应用展示了该模型在捕捉零膨胀和高度偏态非负数据中复杂模式的能力。为支持实际应用，我们开发了新的BCSreg R软件包，实现了所有提出的方法。