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1、參數(shù)估計(jì)(復(fù)習(xí))通過(guò)對(duì)樣本的處理，對(duì)總體的未知參數(shù)（如：數(shù)學(xué)期望、方差等）作出較好的估計(jì)．一．點(diǎn)估計(jì)量的求法：1．矩法：①參數(shù)：設(shè)或稱為參數(shù)②點(diǎn)估計(jì)：設(shè)參數(shù)未知?jiǎng)t構(gòu)造統(tǒng)計(jì)量去估計(jì)稱為的估計(jì)量，為的估計(jì)值，估計(jì)量、估計(jì)值統(tǒng)稱估計(jì)。這種對(duì)未知參數(shù)的定值估計(jì)稱為點(diǎn)估計(jì)。③矩法：用樣本矩一般步驟是：設(shè)，其中參數(shù)待估．（i），計(jì)算；（ii）由=或即：即：有個(gè)估計(jì)量例：（Ｐ110）設(shè)=，求otherstaffoftheCentre.Duringthewar,ZhuwastransferredbacktoJiangxi,andDirectorofthenewOff
2、iceinJingdezhen,JiangxiCommitteeSecretary.Startingin1939servedasrecorderoftheWestNorthOrganization,SecretaryoftheSpecialCommitteeAfterthevictoryofthelongMarch,hehasbeentheNorthwestOfficeoftheFederationofStateenterprisesMinister,ShenmufuguSARmissions,DirectorofNingxiaCountyparty
3、CommitteeSecretaryandrecorderoftheCountypartyCommitteeSecretary,Ministersand１９。解：由于=；又=則由＃2．極大似然法設(shè)，其中未知，則：，得的聯(lián)合分布稱為似然函數(shù)解題方法：將似然函數(shù)取對(duì)數(shù)，有：對(duì)上式求偏導(dǎo)，并令由k元方程組（似然方程組）求得例：(P118)設(shè)，概率密度為=，，試求的極大似然估計(jì)．otherstaffoftheCentre.Duringthewar,ZhuwastransferredbacktoJiangxi,andDirectorofthenewOffice
4、inJingdezhen,JiangxiCommitteeSecretary.Startingin1939servedasrecorderoftheWestNorthOrganization,SecretaryoftheSpecialCommitteeAfterthevictoryofthelongMarch,hehasbeentheNorthwestOfficeoftheFederationofStateenterprisesMinister,ShenmufuguSARmissions,DirectorofNingxiaCountypartyCom
5、mitteeSecretaryandrecorderoftheCountypartyCommitteeSecretary,Ministersand１９解：的似然函數(shù)為兩邊取對(duì)數(shù)，得：似然方程為即：的極大似然估計(jì)量為＃例：(P120)設(shè)在上服從均勻分布，，求的極大似然估計(jì)量．解：的分布密度為：∴ 似然函數(shù)為：顯然對(duì)無(wú)法利用令偏導(dǎo)數(shù)等于零的方法求駐點(diǎn)，使得在某點(diǎn)處有：事實(shí)上：由，即：所以在上，為的最大值．故得的極大似然估計(jì)量為：＃otherstaffoftheCentre.Duringthewar,ZhuwastransferredbacktoJiang
6、xi,andDirectorofthenewOfficeinJingdezhen,JiangxiCommitteeSecretary.Startingin1939servedasrecorderoftheWestNorthOrganization,SecretaryoftheSpecialCommitteeAfterthevictoryofthelongMarch,hehasbeentheNorthwestOfficeoftheFederationofStateenterprisesMinister,ShenmufuguSARmissions,Dir
7、ectorofNingxiaCountypartyCommitteeSecretaryandrecorderoftheCountypartyCommitteeSecretary,Ministersand１９3．順序統(tǒng)計(jì)量法：①總體均值的估計(jì)：設(shè) 記中位數(shù)可用：作為總體的中位數(shù)的估計(jì)量若總體為連續(xù)型且對(duì)稱時(shí)，的中位數(shù)就是均值，即：該方法稱為數(shù)學(xué)期望的順序統(tǒng)計(jì)量估計(jì)法例：設(shè)燈泡壽命，為估計(jì)平均壽命，隨機(jī)取，試用順序統(tǒng)計(jì)量法估計(jì)．解：觀測(cè)值的順序統(tǒng)計(jì)量為：，所以＃注：該方法的優(yōu)點(diǎn)是不易受個(gè)別離群值的影響．②總體標(biāo)準(zhǔn)差的估計(jì)：設(shè)那么，總體的標(biāo)準(zhǔn)差可用樣本極差
8、估計(jì)，即：為極差估計(jì)法。注：方法粗糙，當(dāng)n較大時(shí)，遠(yuǎn)不如用S或估計(jì)的可靠．一．估計(jì)量的評(píng)選標(biāo)準(zhǔn)：由于 的隨機(jī)
