This　paper　introduces　a　novel　family　of　distributions　known　as　generalized　scale　mixtures　of　generalized　normal　distributions　(GSMGN).　These　distributions　incorporate　two　additional　shape　parameters　that　serve　to　regulate　the　shape　and　tails　of　the　distribution.　A　finite　mixture　model　based　on　this　family　is　presented　to　address　clustering　heterogeneous　data　in　the　presence　of　leptokurtic　and　heavy-tailed　outcomes.　The　estimation　of　the　parameters　of　this　model　are　obtained　by　developing　an　ECM-PLA　ensemble　algorithm　which　combine　the　profile　likelihood　approach　(PLA)　and　the　classical　Expectation　Conditional　Maximization　(ECM)　algorithm,　and　the　observed　information　matrix　is　obtained.　The　applicability　of　this　new　family　and　the　numerical　performance　of　the　proposed　methodology　is　discussed　through　simulated　and　real　data　examples.