A Novel Finite Mixture Model Based on the Generalized t Distributions with Two-Sided Censored Data

Abstract

In light of the rapid technological advancements witnessed in recent decades, numerous disciplines have been inundated with voluminous datasets characterized by multimodality, heavy-tailed distributions, and prevalent missing information. Consequently, the task of effectively modeling such intricate data poses a formidable yet indispensable challenge. This paper endeavors to address this challenge by introducing a novel finite mixture model predicated upon the generalized t distribution, tailored specifically to accommodate two-sided censored observations, thereby establishing a foundational framework for modeling this complex data structure. To facilitate parameter estimation within this model, we devise a variant of the EM-type algorithm, amalgamating the profile likelihood approach with the classical Expectation Conditional Maximization algorithm. Notably, this hybridized methodology affords analytical expressions in the E-step and a tractable M-step, thereby substantially enhancing computational expediency and efficiency. Furthermore, we furnish closed-form expressions delineating the observed information matrix, pivotal for approximating the asymptotic covariance matrix of the MLEs within this mixture model. To empirically evaluate the efficacy of the proposed algorithm, a series of simulation studies are conducted, demonstrating promising performance across various artificial datasets. Additionally, the practical applicability of the proposed methodology is elucidated through its deployment on two real-world datasets, thereby underscoring its feasibility and utility in practical settings.