Finite mixture models have been widely used to model and analyze data from heterogeneous populations. In practical scenarios, these types of data often confront upper and/or lower detection limits due to the constraints imposed by experimental apparatuses. Additional complexity arises when measures of each mixture component significantly deviate from the normal distribution, manifesting characteristics such as multimodality, asymmetry, and heavy-tailed behavior, simultaneously. This paper introduces a flexible model tailored for censored data to address these intricacies, leveraging the finite mixture of skew-t distributions. An Expectation Conditional Maximization Either (ECME) algorithm, is developed to efficiently derive parameter estimates by iteratively maximizing the observed data log-likelihood function. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of truncated skew-t distributions. Moreover, a method based on general information principles is presented for approximating the asymptotic covariance matrix of the estimators. Results obtained from the analysis of both simulated and real datasets demonstrate the proposed method’s effectiveness.

有限混合模型已广泛用于建模和分析来自异质群体的数据。在实际场景中，由于实验设备的限制，这些类型的数据经常面临检测上限和/或下限。当每个混合成分的测量值显着偏离正态分布，同时表现出多模态、不对称和重尾行为等特征时，就会出现额外的复杂性。本文介绍了一种针对审查数据量身定制的灵活模型，利用倾斜分布的有限混合来解决这些复杂问题。开发了期望条件最大化任一 (ECME) 算法，通过迭代最大化观察到的数据对数似然函数来有效地导出参数估计。该算法在 E 步具有闭合形式表达式，依赖于截断偏斜分布的均值和方差公式。此外，提出了一种基于一般信息原理的方法来逼近估计量的渐近协方差矩阵。对模拟和真实数据集的分析获得的结果证明了所提出方法的有效性。