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，目前文献中仅探讨了该类分布中少数特定模型在回归中的应用，且尚未正式提出零调整扩展。本文系统阐述了Box-Cox对称回归模型类，并引入了一种适用于含不可忽略零值观测数据建模的新型零调整扩展。我们讨论了极大似然估计方法，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量在内的诊断工具。以基础教育支出为对象的实证应用展示了该模型在零膨胀和高度偏态非负数据中捕捉复杂模式的能力。为支持实际应用，我们开发了新的R软件包BCSreg，实现了所有提出的方法。