1、中國科學技術大學博士學位論文次序統(tǒng)計量和多維伯努利隨機向量的相依結構姓名：謝朝德申請學位級別：博士專業(yè)：數(shù)學（概率論與數(shù)理統(tǒng)計）指導教師：胡太忠20060401AbstractIneverydaylife，peopleusuallyuserandomvariablesorrandomvectorstodescribeun—certainfactorsaboutthingsandtheirdevelopmentWhilethcdepend

2、enceandrestrictionsamongtheuncertainfactors，therandomvariablesorrandomvectors，thatinfhtettcdthingsandtheirdevelopmentbecomethemainresearchobjectsofthestochasticdependencethe—oryThepurposeofthispaperistoinvestigateseveral

3、positiveand／ornegativedependencepropertiesabouttwospecialmultivariaterandomvectorsordinaryorderstatisticsandtheBernoullirandomvectorsFirstly，foroccupancynumbervectorB=(B1，B2，，Bn)inthebailsandbinsexper—iment，weprovethatE【

4、妒(Bz)IBl≥bz，Ba≤bj，BK=bK】isdecreasinginnonnegativevectorsb』，bJandbKforallincreasingfunctions0璃_跣，wheretheconditionalexpec—tationsareassumedtoexist，I，，，Ⅳ，Larefourdisjointsubsetsof(1，2，n，andoneortwoof，，，andKmaybeanemptysetI

5、nparticular，WegetthatBisNRD，NRTDandNLTDByapplyingsuchproperties，weinvestigatefurtherdependencestructuresoforderstatisticsXl、n≤X2n≤曼XMlofnindependentrandomvariablesXl，X2，，XnwithpossiblydifferentdistributionsForl≤t：221、瑪2：

6、％茁“，％棚ztJ爿拼‘S)isincreasingins，andthatifeventA郴iseither(Xi：。S)orXinss)thenⅡ)(局lnJJl，瑪2：nz2，XjrnXr[Ai，s)isdecreasinginzforfixedSItisalsoshownthatinthissituation，ifeachXkhasacontinuousdistributionfunctionthenAi，scanbechosen

7、tobeeitherx一1n5x㈨)or(xm=5)WethuscomplementandextendstoneresultsinDubhashiandRanjan(1998)andBolandetal(1996)Secondly，multivariateBernoullirandomvectorshavemanyapplicationsinseveralfieldsTheilprobabilitymassfunctionsareasp

8、ecialweightedtreeprobabilitytreeWeutilizeanewlydevelopedtool，majorizationwithrespecttowcightedtrees，toestablishthesufficientandnecessaryconditionsforrnultivariateBernoullirandomvectorstopossesssomenegativeandpositivedepe