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1、12-5-22Poissondistribution-Wikipedia,thefreeencyclopediaPoissondistributionFromWikipedia,thefreeencyclopediaInprobabilitytheoryandstatistics,thePoissondistributionPoisson(pronounced[pwasɔ̃])isadiscreteprobabilitydistributionthatexpressesProbabilitymassfunctiontheprobabilityo
2、fagivennumberofeventsoccurringinafixedintervaloftimeand/orspaceiftheseeventsoccurwithaknownaveragerateandindependentlyofthetimesincethelastevent.[1](ThePoissondistributioncanalsobeusedforthenumberofeventsinotherspecifiedintervalssuchasdistance,areaorvolume.)Supposesomeonetyp
3、icallygets4piecesofmailperday.Thatbecomestheexpectation,buttherewillbeacertainspread:sometimesalittlemore,sometimesalittleless,onceinawhilenothingatall.[2]Givenonlytheaveragerate,foracertainperiodofobservation(piecesofmailperday,phonecallsperhour,etc.),andassumingthattheproc
4、ess,ormixofprocesses,thatproducetheeventflowareessentiallyrandom,thePoissondistributionspecifieshowlikelyitisthatthecountwillbe3,or5,or11,oranyothernumber,duringoneperiodofobservation.Thatis,itpredictsthedegreeofspreadaroundaknownaveragerateofoccurrence.[2]Thehorizontalaxisi
5、stheindexk,thenumberofoccurrences.ThefunctionisonlyThedistribution'spracticalusefulnesshasbeenexplainedbythePoissonlawofsmallnumbers.[3]definedatintegervaluesofk.Theconnectinglinesareonlyguidesfortheeye.ContentsCumulativedistributionfunction1History2Definition3Properties4Rel
6、ateddistributions5Occurrence5.1Howdoesthisdistributionarise?—Thelawofrareevents5.2Multi-dimensionalPoissonprocessen.wikipedia.org/wiki/Poisson_distribution1/1312-5-22Poissondistribution-Wikipedia,thefreeencyclopedia5.3Otherapplicationsinscience6GeneratingPoisson-distributedr
7、andomvariables7Parameterestimation7.1Maximumlikelihood7.2Confidenceinterval7.3Bayesianinference8Seealso9Notes10ReferencesHistoryThedistributionwasfirstintroducedbySiméonDenisPoisson(1781–1840)Thehorizontalaxisistheindexk,theandpublished,togetherwithhisprobabilitytheory,in183
8、7inhisworkRecherchessurlaprobabilitédesjugementsenmatièrecriminelleetennumb
