统计学数理统计在统计学中的地位The position of statistical mathematical statistics in Statistics.docx
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统计学数理统计在统计学中的地位The position of statistical mathematical statistics in Statistics.docx
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统计学数理统计在统计学中的地位ThepositionofstatisticalmathematicalstatisticsinStatistics
统计学-数理统计在统计学中的地位(ThepositionofstatisticalmathematicalstatisticsinStatistics)
I.Themaincharacteristicsofmathematicalstatisticsandstatistics
(1)themainfeaturesofmathematicalstatistics;
Themathematicalstatisticsisbasedontherandomphenomenonlimitedincomeobservationsorexperimentaldatasummarized,findrulesofthelimiteddata,andthenumberofrulesbasedonthecorrespondingoverallphenomenonmakeasubjectinferenceorjudgment.Summarizedasfollows:
first,randomness,thatistosay,theobjectofmathematicalstatisticsshouldbestochastic,deterministicphenomenonisnotthecontentofmathematicalstatistics.Twoislimited,thatistosay,thenumberofrandomphenomenainmathematicalstatisticsislimitedbythenumberoftimes.Thethreeisquantitative,thatis,mathematicalstatisticstostudytherandomphenomenonofthenumberofregularitybased,andthequalityofrandomphenomenaforthesecondtime.Fouristheresearchmethodused,mainlyforinduction.Finally,mathematicalstatisticshasacertainprobabilityreliabilitythroughthestudyofsmallsamplesinordertoachievetheoverallinference.Thattheoverallerrorsampleisanobjectiveexistence,butstatisticsnotonlyfocusonthesizeoftheerror,theerrorpossibilityalsopointedout.
Accordingtothecharacteristicsofmathematicalstatistics,mathematicalstatisticsisoneofthemostimportantandactivesubjectsinappliedmathematics.Thus!
Statisticsfromthedisciplinedivision,shouldbelongtomathematics,butitfocusesonapplication!
Insteadofpuremathematicaltheoryormethodofresearch,themethodsusedarefocusingoninduction,ratherthanmathematicaldeduction.
Insummary,themaincharacteristicsofmathematicalstatisticscanbesummarizedinonesentence,mathematicalstatisticsisalimitednumberofobservationsorexperimentsanumberofresearchresultsofrandomphenomena,accordingtothenumberofgeneralrulesmaketheappliedmathematicshascertainreliabilityinference.
(two)themaincharacteristicsofStatistics
Statisticsisamethodologyscienceofcollecting,arrangingandanalyzingstatisticaldata.Thepurposeofstatisticsistoexploretheinternalquantityandregularityofdatasoastoachievescientificunderstandingofobjectivethings.
Statisticsfromthescopeofitsresearch,therearethreemajorareas:
datacollection,datacollationanddataanalysis.Firstofall,withthedevelopmentofstatistics,itisdifficulttotellwhichareasaremoreimportantinthesethreefields.Perhapsalotofpeoplethinkthatdataanalysisismoreimportant.IntheanalysisoftheUnitedStatesin1910and1900twoagriculturalcensusdata,Leninpointedout:
"allproblems,allthedifficulttaskishowthesedatacanexactlyfromthepoliticalandeconomicsituationthatthedifferentkindsortypesoffarmers."Thisshowstheimportanceofdatacollation.Studyonanalysismethodofdistressstatisticsinourcountryisnotdatainrecentyears,butthelackofadequatestatisticaldatavalid,whichcannotbeconfirmedortotestthecorrespondingeconomictheory,economicmodelandeconomicpolicydata.Theimportanceofdatacollectionisevident.Second,statisticsisamethodologicalscience.Foralongtime,ithasbeenconsideredthatthebasicmethodsofstatisticalresearcharenumerousobservationmethod,statisticalindexmethod,statisticalgroupingmethodandmodelinferencemethod.Especiallyalotofobservationbecomesoneofthemostimportantbasiccharacteristicsofstatisticalmethods,itcanbesaidthatthisisoneofthefundamentaldifferencebetweenstatisticalandmathematicalstatisticsorstatisticsalsoreallyhasbecomethemodernWesternMathematicalStatistics.Withthestatisticsfromthepurelystatisticaldescriptionoftheearlydevelopmentforbothdescriptivestatisticsandinferentialstatistics,untilsomescholarsthinkthatthemodernstatisticsshouldbedominatedbystatisticalinference,supplementedbydescriptivestatistics,regardlessofwhethertheideainappropriate,butitcanbeinferredstatisticallyhasplayedanimportantroleinthemodernsociallife.Infact,inferentialstatisticshasbecomeoneofthebasicfeaturesofmodernstatistics.Again,thestatisticsfromonedaybecomeascience,thephenomenonofquantityresearchasthebasiccharacteristics,butalsotheirown,emphasizedtheneedforaqualitativeunderstandingofthephenomenonasthefoundation.
(three)comparisonofmathematicalstatisticsandstatistics
Throughtheaboveanalysisofmathematicalstatisticsandstatisticalcharacteristics,themainsimilaritiesanddifferencesbetweenmathematicalstatisticsandstatisticscanbesummarizedasfollows:
1.fromtheobjectivepointofview,bothfocusingonthenumberoflawrevealsthegeneralphenomenon,andwasclaimedtobemorequalitativetotheoverallunderstandingofthephenomenonasthefoundation.
2.fromthewayofstudy,throughtheresearchonquantitativecharacteristicsoftheindividualpartofoverallhopeofmathematicalstatistics,inordertoachievetheoverallrecognitionofthecorrespondingnumberoffeatures;andbothstatisticsbyresearchingonquantitativecharacteristicsofthegeneralstructureofallindividuals(ifpossibleor$worthit),inordertoachievetheoverallunderstandingthecorrespondingnumberoffeatures,alsohopethatthroughtheresearchofquantitativecharacteristicsoftheindividualpartsoftheoverall,
Inordertoachieveanunderstandingofthecorrespondingquantitativecharacteristicsofthepopulation.
3.fromtheresearchmethods,thecorrespondingcharacteristicsofmathematicalstatisticsmainlydependsonthecharacteristicsofsmallsamplestatisticalmathematicsprincipletoinfertheoveralldistributionofvalue;andstatisticsorthecorrespondingcharacteristicsofstatisticalinferencemainlydependsontheeigenvaluesoflargesamplestatisticalmathematicsprincipletoinfertheoverallvaluedistribution.
4.fromthemainscopeoftheirresearch,mathematicalstatisticsfocusedonquantitativeanalysisofthesamplesandstatistics;notonlypaysattentiontothequantitativeanalysisofthesampledata,andattentionontheoverallanalysis,quantitativeobtainedallthedataatthesametime,theresearchmethodsofdatacollectionanddataprocessingmethod.
5.fromthemathematicaldeductionoftheoveralluseofsampledata,theprobabilitytheoryisthecommonfoundation.Especiallyasoneofthebasicmethodsofstatisticalmethodofmassobservation,itsmathematicalbasisisthelawoflargenumbersinthetheoryofprobabilitystatistics;largesamplecanbeeasilyinferredfromthemathematicalbasisofgeneralcharacteristicsofitisthecentrallimittheoreminprobabilitytheory,andwhetheritisthelawoflargenumbersorthecentrallimittheoremisalsothefoundationofmathematicalstatistics.
Althoughthe6.statisticsemphasizetheapplication,butitisamathematicaldiscipline,focusingontheapplicationofthemethodbasedonmathematicalstatistics;moreemphasisonresearchandapplicationofanalysismethodtosolvetheproblemofsocialeconomicandthenumberofscientificresearchandthemathematicalbasisofthemethoditself,bythetheoryofstatisticscorrespondingtoinfact,research,scientificresearchonthemathematicalbasisofstatisticalinferencemethod,isoneoftheresearchareasofmathematicalstatistics.
Fromtheabovecharacteristicsandcomparisonofmathematicalstatisticsandstatistics,canseeclearlythatwiththedevelopmentofmodernstatisticsandinthesocialpoliticalandeconomiclifeplayagrowingroleinthetrend,ideasandmethodstostudytheissueofmathematicalstatisticsonthedevelopmentofstatisticshasproducedrevolutionaryinfluence,butimportant,mathematicalstatisticsandstatisticsaretwosubjectsdifferent,cannotsimplybe"unified".
Two,thestatusofmathematicalstatisticsinStatistics
Statisticsandstatisticsaretwodifferentdisciplines,theycannotreplaceeachother,cannotbelikeovertheyearssomescholarsproposedthat,toestablishastatisticalmatter,ortheintegrationofstatistics,itsessenceistocombinemathematicalstatisticsandstatistics.Butthedirectconsequencesoftheirfusionisnowusedbysomecollegesanduniversitiesinstatisticstextbooks,bothhavestatisticalcontent,therearestatisticalcomponents,weinfact,neitherfishnorfowl,simplesplicingcontentandcontentisthestatisticsofthestatistics.ThisisasadthingaboutChina'sstatistics,statisticstextbooksandstatisticalteachinginrecentyears:
losingoneselfandblindlywantingtoconnectwiththewest".Theauthorbelievesthatinordertostraightenouttherelationshipbetweenmathematicalstatisticsandstatistics,itisnecessarytomakeathoroughstudyofthestatusofmathematicalstatisticsinstatistics.
(1)thestatusofmathematicalstatisticsinthedevelopmentofstatisticalthinking
Statistics,asasocialpractice,hasahistoryofseveralthousandyears.Itispeople'ssimpleunderstandingofstatistics.Withthecontinuousdevelopmentofsocialproductivity,thecontemporarystatisticshasnotimprisonandplantotheunificationof"category.
1.statisticsitisrecognizedasoneofthemostpowerfulweaponsofthesociety,hasbeenwidelyappliedinmanyfieldsofsociety,politics,economy,scienceandtechnology,andeachareahasitscomplexityanddiversity,thesimple"unification",namelyacomprehensivesurveyisalmostimpossible,butfullyunderstandtheregularityofcontactnumberthebasicsituationofeveryareaanddifferentareas,necessaryformodernsocia
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- 统计学数理统计在统计学中的地位The position of statistical mathematical statistics in 统计学 数理统计 中的 地位 The
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