Peculiarity　oriented　mining　(POM),　aimed　at　discovering　peculiarity　rules　hidden　in　a　dataset,　is　a　data　mining　method.　Peculiarity　factor　(PF)　is　one　of　the　most　important　concepts　in　POM.　In　this　paper,　it　is　proved　that　PF　can　accurately　characterize　the　peculiarity　of　data　sampled　from　a　normal　distribution.　However,　for　a　general　one-dimensional　distribution,　it　does　not　have　the　property.　A　local　version　of　PF,　called　LPF,　is　proposed　to　solve　the　difficulty.　LPF　can　effectively　describe　the　peculiarity　of　data　sampled　from　a　continuous　one-dimensional　distribution.　Based　on　LPF,　a　framework　of　local　peculiarity　oriented　mining　is　presented,　which　consists　of　two　steps,　namely,　peculiar　data　identification　and　peculiar　data　analysis.　Two　algorithms　for　peculiar　data　identification　and　a　case　study　of　peculiar　data　analysis　are　given　to　make　the　framework　practical.　Experiments　on　several　benchmark　datasets　show　their　good　performance.