The　statistical　inference　for　minimum　distance　parametric　estimation　has　been　well　developed　in　recent　years,　concerning　the　asymptotic　behaviors　of　the　minimum　L1-distance　estimator,　minimum　L2-distance　estimator　and　minimum　Skorohod-distance　estimator.　The　question　is　how　to　realize　the　numerical　solution　of　the　minimum　Skorohod-distance　estimator,　due　to　its　complicated　analytic　structure.　This　paper　aims　to　discuss　the　minimum　distance　estimation　problem　for　Poisson　processes.　The　main　contribution　includes　the　consistency　and　the　approximate　numerical　solution　of　the　minimum　Skorohod-distance　estimator,　accompanied　with　the　study　of　the　minimum　L1-distance　estimator　and　minimum　L2-distance　estimator.　In　the　numerical　examples,　three　estimators　exhibit　the　consistency　trend.　The　mean　square　error　of　the　minimum　L1-distance　estimator　and　minimum　L2-distance　estimator　are　comparable　to,　or　superior　to　the　minimum　Skorohod-distance　estimator　in　the　regular　cases,　while　the　results　are　reversed　in　the　change-point　case.　The　bias　of　the　minimum　Skorohod-distance　estimator　is　either　superior　or　comparable　to　the　others　in　the　regular　cases.　　©　Published　under　licence　by　IOP　Publishing　Ltd.