The　measurement　of　liquidity　based　on　low-frequency　data　is　a　crucial　issue　in　the　financial　market　microstructure　literature.　This　paper　extends　the　commonly　used　LOT　liquidity　model　by　incorporating　the　characterization　of　the　volatility　dynamics　and　distributional　properties　of　return　series,　thereby　significantly　improving　both　the　goodness-of-fit　of　liquidity　model　and　the　estimation　performance　of　the　existing　low-frequency　liquidity　measures.　The　new　models,　which　have　a　special　form　of　heavy-tailed　Censored-GARCH　model,　have　challenges　in　estimation.　We　then　provide　an　approximate　maximum　likelihood　estimation　method　to　circumvent　this　problem.　A　real　data　analysis　is　conducted　to　evaluate　the　performance　of　the　new　liquidity　measures.　The　results　show　overwhelming　evidence　that　our　new　measures　have　advantages　over　the　existing　measures　in　both　estimation　error　and　correlation　coefficient　with　high-frequency　bid-ask　spread.　The　robustness　check　analysis　further　illustrates　that　the　advantages　of　our　new　measures　are　stable　across　different　stock　industries　and　different　turnover　levels.