几何分布样本间隔的似然比序

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1、几何分布样本间隔的似然比序张艺赢,赵鹏兰州大学数学与统计学院，兰州　730000摘要：文献中，对于指数分布的样本间隔已有大量的研究结果。众所周知，几何分布是指数分布的离散对应情形，但目前为止尚未见到几何分布的样本间隔的任何结果。本文在似然比序意义下研究了几何分布的样本间隔的随机比较问题，具体来说，我们建立了如下结果：当两组几何参数向量满足弱超优序时，其对应的样本间隔之间满足似然比序，此结果实际上与指数情形是相互对应的。关键词：几何分布;样本间隔；似然比序；超优序中图分类号：O211.9LikelihoodR

2、atioOrderonSampleRangesofGeometricdistributionZHANGYiying,ZHAOPengSchoolofMathematicsandStatistics,LanzhouUniversity,Lanzhou730000Abstract:Intheliterature,thereexistsmuchworkonsamplerangesfromexponentialdistributions.Itiswellknownthatthegeometricdistributi

3、onisthediscretecounterpartofexponentialdistribution.However,thereisnoanyresultonsamplerangessofar.Inthispaper,weinvestigatethelikelihoodratioorderofsamplerangesarisingfromgeometricdistribution.Specifically,itisshownthat,iftheweakmajorizationorderholdsbetwee

4、nthetwoparametervectors,thenthelikelihoodratioorderholdsbetweenthecorrespondinggeometricsampleranges.Thisresultestablishedhereactuallycorrespondstotheexponentialcase.Keywords:Geometricdistribution;Sampleranges;Likelihoodratioorder;Majorization0Introductio

5、nOrderstatisticsandthosestatisticshavingacloserelationtoorderstatisticsplayapromi-nentroleinmanyareasofprobabilityandstatistics.Inparticular,spacingsareofgreatinterest基金项目：NationalNaturalScienceFoundationofChina(11001112)，ResearchFundfortheDoctoralProgramo

6、fHigherEducation(20090211120019).作者简介：ZHANGYiying（1988-），male，Masterstudent，majorresearchdirection：AppliedProbabilityandStatistics.Correspondenceauthor：ZHAOPeng（1980-），male，associateprofessor，majorresearchdirection：AppliedProbabilityandStatistics,reliabili

7、tytheory,statisticalinference.-2-inmanyareassuchasgoodness-of-fittests,reliabilitytheory,auctiontheory,actuarialscience,lifetesting,operationsresearch,informationsciences,andmanyotherareas.Onemayre-fertoBalakrishnanandRao(1998a,1998b)forsomegoodness-of-fitte

8、stsbasedonfunctionsofsamplespacings.LetX1:n≤X2:n≤···≤Xn:ndenotetheorderstatisticsarisingfromrandomvariablesX1,X2,...,Xn.Then,thek-thorderstatisticXk:nisjustthelifetimeofa(n−k+1)-out-of-nsystem,whichisaverypop