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In the case of censored data, it is often seen that the error distribution is skewed and multimodal. Ordinary least squares (OLS) estimator, which often gives biased and inconsistent results for censored data, and Tobit estimator, which is frequently used in censored data estimation and gives inconsistent results when some assumptions are not met, are also problematic in the presence of skewed and multimodal distribution of error terms. A new estimator is proposed as an alternative to the two conventional estimators used in the case of censored data. For censored regression model, an estimation method, known as partial adaptive or quasi-maximum likelihood estimator, has been introduced based on the alpha skewed logistic distribution, which is a flexible error distribution. According to the bias and mean square error (MSE), new estimator is superior for estimating the coefficients of the censored regression model under the skewed and multimodal error distribution.