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1、DOI：10.13209/j.0479-8023.2000.083北京大学学报(自然科学版),第36卷,第5期,2000年9月ActaScientiarumNaturaliumUniversitatisPekinensis,Vol.36,No.5(Sep,2000)SomeResultsonMLEoftheParameteroftheExponentialDistributionfromRandomlyCensoredDataWANGQihua(DepartmentofProbabilityandSta
2、tistics,SchoolofMathematicalSciences,Beijing,100871)AbstractConsidertheexponentialpopulationx-F(x,H)=1-eH,x ,whereH>0isanunknownparameter.InthispapertheMLEofH,sayH^n,fromrandomlycensoreddataisprovedtobeasymptoticminimaxefficiency.Thatis,foracertainlossf
3、unctionw(#),(n)-1limlimsupEHc{w[<(n)(H^n-Hc)]}=Ew(N),Dy0ny]
4、Hc-H
5、6、,respectively.Keywordsasymptoticminimaxefficiency;interativelogarithmlaw;meanerror0IntroductionLetX1,X2,,,Xnberandomvariablesdenotingsurvivaltimewithacommondistributionfunctionx-F(x,H)=1-eH,x ,H>0,(1)whereHistheunknownparameter.Thereareextensivelystudie
7、soninferenceontheparameterHwithcompletesample(see,[1][2][3][4][5]e.g.,BainandEngelhardt,EI-Sayyad,Harltor,SarhanandGreenberg,Epstein)a-mongothers.Ofteninreliabilitystudies,itemsaresubjectedtocensoringwhenonewishtoesti-matesomestatisticcharacteristicofthe
8、lifedistributionofadevicewhichhasaratherlonglifetimeduringcertaintypesoflifetesting.InboththecasesofTypeÑandTypeÒcensoredlifetesting,manyestimationproceduresandinferentialtechniqesbasedonthemaresuggestedbysomeauthors收稿日期:1999-06-29;修回日期:1999-12-25584北京大学
9、学报(自然科学版)第36卷[1][6][7][8](see,e.g.,BainandEngel-hardt,DeemerandVotaw,Lawless,MoorandBilikam,[9][10]Halperin,Cox,andothers).Here,therightrandomcensoringmodelisconsidered,thatis,associatedwitheachfailuretimeXifromtheexponentialpopulationthereisanindependen
10、tnonegativecensoringtimeYiandY1,Y2,,,YnareassumedtobeiidrandomvariableswithdistributionfunctionG.Theobserveddatainthismodelarethepairs(Zi,Di),whereZi=min(Xi,Yi),Di=I[Xi[Yi],i=1,2,,,n,andI[#]istheindicatorfunctionofacertain
