Finitemixturesoflog-normalsprovetobeveryusefulwhenanalysinginequalityandinequalitydecomposition.Firstof all, under suitable prior information, we can try to identify each member of the mixture with a social group according to itsincomelevel.Second,usingdecomposableindices,wecananalyseinequalityinsideeachgroupandbetweenthegroups identified by the mixture. Finally, the possibility of Rao-Blackwellization can help to improve the precision of inference resultsfortheseindices,knowingthatafinitemixtureoflog-normalsprovidesconditionalanalyticalresultsforconditional momentsoftheseindices.