關(guān)于統(tǒng)計(jì)分布的次序統(tǒng)計(jì)量的隨機(jī)序.pdf

1、復(fù)旦大學(xué)碩士學(xué)位論文關(guān)于統(tǒng)計(jì)分布的次序統(tǒng)計(jì)量的隨機(jī)序姓名：黃永軍申請學(xué)位級(jí)別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計(jì)指導(dǎo)教師：張新生20060508ABSTRACTStochasticorderoforderstatisticsfromheterogeneousrandomsamplesisnowapopulartopicofresearch，whichhasbeenfoundnumerousapplicationsinmanyareassucha

2、sreliabilitycomparisonofexperiments，economicandSOonInthispaper，wemakeresearchsonstochasticordersoforderstatisticsfromlifedistributionswithproportionalhazards，acceleratinglifedistributionsandnormaldistributions，andobtains

3、omenewresultsInchapter2，letX1，，墨，耐，，弼beindependentnonnegativerandomvariableswith砥一只(。)=1一exp(一九R(z))and。W一日(z)=1一exp(～智R(z))，i=1，，nLetx()2(墨1)，，五n))andxj=(確)，，x函)betheorderstatisticsof(噩，，xn)，(—W，”，揮)，respectivelySuppose

4、thatthereexistsastrictlymonotonefunctionfsuchthat(f(A1)，，f(An))蘭。(，(A：)，，，(A：))，weprovethat：(i)if，’(。)，”(z)≥0，thenXo≥stxjand—墨1)≥扣x矗)；(扼)if，’@)，”(z)≤0，thenX(1)s押。x矗1；(iii)if廠’(z)，”(z)≤0andIxf”(茁)l≤If’(。)I，thenXm)≥武Y南1Wea

5、lsogeneralizetheseresultstoamuchwiderparameterspaceMoreoverletX1lxRIxflX：beindependentWeibuilrandomvariableswithcommonscaleparameterA(A0)andshapeparametersQ1，，an，Q；，，OLn‘，respectivelyWeobtainthat(O[1，，on)三m(＆：，，口：)implie

6、sthatXO)≤stH)andY_)≥?！陎五)Inchapter3，letX1，，k，xf，，霹beindependentnonnegativerandomvariableswith五～只(茁)=1exp(一R(Aix))，胃一日(z)=1exp(一只(A；z))，i=1，，n，whereR(z)=臂r(t)dt，xr(x)isincreasingSupposethatthereexistsastrictlvmonot。nefunc

7、tionfsuchthat(f(A1)，，f(A。))蘭。(，(Ai)，，，(K))，weprovethat：(i)foranyzo，if耥isdecreasinginA，thenXO≥時(shí)xj；(“)forany。o，if耥is協(xié)creasinginA，th8n五1)≤“xa)；(iii)forazlyz0，if麗菥苧熬麗isdecreasinginA，‘hen五n)2atx南；(曲)foranyz0，if麗商％嘗擊嘶isincreas