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.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2024.