We present a unified parametric framework for modal regression applicable to continuous positive distributions, with explicit support for right-censored observations. The key contribution is a systematic analytical reparameterization of density parameters as direct functions of the conditional mode. This closed-form mapping is derived for the Gamma, Beta, Weibull, Lognormal, and Inverse Gaussian distributions, directly linking the mode to a linear predictor. Maximum likelihood estimation is performed using the censored log-likelihood, with asymptotic inference based on the observed Fisher information matrix. A Monte Carlo simulation study across multiple distributions, sample sizes, and censoring levels confirms consistent parameter recovery. Empirical bias and RMSE decrease as expected, and Wald confidence intervals achieve nominal coverage. Finally, the proposed methodology is illustrated through an application to real-world reliability data. All methodology is implemented in the open-source R package ModalCens.

翻译：本文提出一个适用于连续正分布的参数化众数回归统一框架，并明确支持右删失观测。核心贡献在于通过系统性的解析重参数化方法，将密度参数直接表达为条件众数的函数。针对Gamma分布、Beta分布、Weibull分布、对数正态分布及逆高斯分布推导了封闭形式的映射关系，从而将众数与线性预测变量直接关联。基于删失对数似然函数进行最大似然估计，并利用观测Fisher信息矩阵进行渐近推断。通过涵盖多种分布、样本量及删失水平的蒙特卡洛模拟研究，证实了参数估计的一致性：经验偏差与均方根误差如预期下降，Wald置信区间达到名义覆盖水平。最后，通过实际可靠性数据的应用案例展示了所提方法。全部方法已在开源R软件包ModalCens中实现。