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New exponentiated generalized censored regression models: Monte Carlo simulation and application

The standard maximum likelihood estimator of censored regression models is constructed under the assumption of the normal distribution and it yields inefficient results in case of non‐normal asymmetric data or/and presence of outlier(s). In the analysis of censored real‐life data encountered in many disciplines such as finance, medical sciences, and engineering, there is often a violation of the assumption of normality. In this paper, we propose a generalization of the censored normal regression based on the extended normal distribution (EGT). The generalized model, with two additional shape parameters as a and b, includes classical Tobit model for a = 0 and b = 0 and Alpha‐Power Tobit model for a = 1. It provides very flexible estimation in cases symmetric‐asymmetric data and especially in case non‐normal asymmetric data or/and presence of outlier(s). In addition, Lehmann type II‐G Tobit model (LTII‐GT) is also proposed for b = 1 as a special case of generalization. The performance of proposed two new generalizations of Tobit, namely EGT and LTII‐GT has been compared with Tobit, Alpha‐Power Tobit, and classical estimators by means of a comprehensive Monte Carlo simulation study. The performance of proposed models' ML estimators is illustrated on a real data set. The superiority of the proposed estimators is shown.