Evaluation of a robust and asymmetric class of nonlinear regression models under censoring

Censored nonlinear regression models are often based on Gaussian errors for analytical convenience. However, real data—such as income levels, HIV viral loads, or agricultural yields—often exhibit asymmetry, heavy tails, outliers, and censored observations, making classical Gaussian models inadequate. In this study, we extend censored nonlinear regression (CNLR) using the two–piece scale mixture of normal (TP–SMN), a flexible distribution that accommodates both asymmetry and excess kurtosis. We develop an EM–type algorithm that allows exact maximum likelihood estimation without stochastic EM methods. The method’s effectiveness is demonstrated on simulated and real datasets, including Ultrasonic and Oil data. The results show that the proposed TP–SMN–CNLR models are robust against asymmetric behavior, outliers and censoring, providing accurate and reliable inference even under challenging data conditions.