方差的參數(shù)估計(jì)和置信區(qū)間估計(jì)

1、正態(tài)總體均值、方差的參數(shù)可能與置信區(qū)間可能P316 例6.5.1 置信區(qū)間可能clear;Y=14.85 13.01 13.50 14.93 16.97 13.80 17.95 13.37 16.29 12.38;X=normrnd(15,2,10,1) % 隨機(jī)產(chǎn)生數(shù)muhat,sigmahat,muci,sigmaci=normfit(X,0.1) % 正態(tài)擬合muhat,sigmahat,muci,sigmaci=normfit(Y,0.1) % 正態(tài)擬合 X = 15.2573 16.3129 12.6644 14.0788 14.4751 12.5737 12.3611 16.862

2、4 15.0225 13.7097muhat = 14.3318sigmahat = 1.5595muci = 13.4278 15.2358sigmaci = 1.1374 2.5657muhat = 14.7050sigmahat = 1.8432muci = 13.6365 15.7735sigmaci = 1.3443 3.0324 P320例6.5.5 置信區(qū)間可能clear;Y=4.68 4.85 4.32 4.85 4.61 5.02 5.20 4.60 4.58 4.72 4.38 4.70;muhat,sigmahat,muci,sigmaci=normfit(Y,0.05)

3、 muhat = 4.7092sigmahat = 0.2480muci = 4.5516 4.8667sigmaci = 0.1757 0.4211 P321 例6.5.6 置信區(qū)間可能clear;Y=45.3 45.4 45.1 45.3 45.5 45.7 45.4 45.3 45.6;muhat,sigmahat,muci,sigmaci=normfit(Y,0.05) muhat = 45.4000sigmahat = 0.1803muci = 45.2614 45.5386sigmaci = 0.1218 0.3454 單正態(tài)總體均值的假設(shè)檢驗(yàn) 方差sigma已知時(shí)P338 例7.

4、2.1 %h,p,ci,zval=ztest(X,mu,sigma,alpha,tail,dim)clear all;X= 8.05 8.15 8.2 8.1 8.25;h,p,ci,zval=ztest(X,8,0.2,0.05) h = 0p = 0.0935ci = 7.9747 8.3253zval = 1.6771 注：p為觀看值的概率ci為置信區(qū)間；zval統(tǒng)計(jì)量值若h=0: 表示在顯著性水平alpha下，不能否定原假設(shè)；若h=1: 表示在顯著性水平alpha下，否定原假設(shè)；若tail=0:表示雙邊假設(shè)檢驗(yàn)；若tail=1:表示單邊假設(shè)檢驗(yàn)（mumu0）；若tail=0:表示單邊假

5、設(shè)檢驗(yàn)（mumu0）；若tail=0:表示單邊假設(shè)檢驗(yàn)（mumu0）；若tail=0:表示單邊假設(shè)檢驗(yàn)（mu(tail為+1)或單邊mu0）；若tail=0:表示單邊假設(shè)檢驗(yàn)（mu0.05） 同意原假設(shè): Poisson分布； P356 例7.4.1clear all;close;bins=1:6;%總體分成的區(qū)間總類obsCounts=2 6 6 3 3 0;%對(duì)應(yīng)區(qū)間上樣本觀測值個(gè)數(shù)n=sum(obsCounts);%總的觀測樣本數(shù)據(jù)expCounts=n*0.1 n*0.2 n*0.3 n*0.2 n*0.1 n*0.1;%對(duì)應(yīng)區(qū)間上的理論頻數(shù) h,p,st = chi2gof(bins

6、,ctrs,bins,frequency,obsCounts,expected,expCounts,nparams,0) %nparams指定分布中待估參數(shù)的個(gè)數(shù) h = 0p = 0.5580st = chi2stat: 1.1667 df: 2 edges: 0.5000 2.5000 3.5000 6.5000 O: 8 6 6 E: 6 6 8 注：h=0（p值0.05） 同意原假設(shè)分布；clear all;bins=1:6;%總體分成的區(qū)間總類obsCounts=2 6 6 3 3 0;%對(duì)應(yīng)區(qū)間上樣本觀測值個(gè)數(shù)n=sum(obsCounts);%總的觀測樣本數(shù)據(jù)expCounts=

7、n*0.1 n*0.2 n*0.3 n*0.2 n*0.1 n*0.1;%對(duì)應(yīng)區(qū)間上的理論頻數(shù)h,p,st=chi2gof(bins,ctrs,bins,frequency,obsCounts,expected,expCounts,frequency,obsCounts,expected,expCounts,frequency,obsCounts,expected,expCounts,frequency,obsCounts,expected,expCounts,frequency,obsCounts,expected,expCounts,frequency,obsCounts,expected

8、,expCounts) %nparams指定分布中待 估參數(shù)的個(gè)數(shù) 注：h=0（p值0.05） 同意原假設(shè)分布；例2 丟擲骰子100次,分不出現(xiàn)的點(diǎn)數(shù)為13次 14次 20次 17次 15次 21次1點(diǎn) 2點(diǎn) 3點(diǎn) 4點(diǎn) 5點(diǎn) 6 點(diǎn)檢驗(yàn)這粒骰子是否均勻？解:均勻,即1點(diǎn)朝上=6點(diǎn)朝上=依照觀測值: 同意,認(rèn)為總體服從均勻分布,這粒骰子是均勻的.bins=1:6;%總體分成的區(qū)間總類obsCounts=13 14 20 17 15 21;%對(duì)應(yīng)區(qū)間上樣本觀測值個(gè)數(shù)n=sum(obsCounts);%總的觀測樣本數(shù)據(jù)lambdaHat=1/6; %參數(shù)的MLE可能值expCounts=n*lam

9、bdaHat n*lambdaHat n*lambdaHat n*lambdaHat n*lambdaHat n*lambdaHat;% 理論頻數(shù)，即均為100/6h,p,st=chi2gof(bins,ctrs,bins,frequency,obsCounts,expected,expCounts,nparams,0) %nparams指定分布中待估參數(shù)的個(gè)數(shù) h = 0p = 0.6692st = chi2stat: 3.2000 df: 5 edges: 0.5000 1.5000 2.5000 3.5000 4.5000 5.5000 6.5000 O: 13 14 20 17 15

10、21 E: 16.6667 16.6667 16.6667 16.6667 16.6667 16.6667 講明：h=0(p值0.05)故同意原假設(shè)，認(rèn)為總體服從均勻分布,這粒骰子是均勻的. 例3 某工廠近5年發(fā)升63次事故,按星期幾分類如下星期 一 二 三 四 五 六 次數(shù) 9 10 11 8 13 12問事故發(fā)生與否與星期幾有關(guān)？解 : 1 2 3 4 5 6 9 10 11 8 13 12 10.5 10.5 10.5 10.5 10.5 10.5同意認(rèn)為事故發(fā)生與星期幾無關(guān).bins=1:6;%總體分成的區(qū)間總類obsCounts= 9 10 11 8 13 12;%對(duì)應(yīng)區(qū)間上樣本觀測

11、值個(gè)數(shù)n=sum(obsCounts);%總的觀測樣本數(shù)據(jù)lambdaHat=1/6; %參數(shù)的MLE可能值expCounts=n*lambdaHat n*lambdaHat n*lambdaHat n*lambdaHat n*lambdaHat n*lambdaHat;% 理論頻數(shù)，即均為63/6h,p,st=chi2gof(bins,ctrs,bins,frequency,obsCounts,expected,expCounts,nparams,0) %nparams指定分布中待估參數(shù)的個(gè)數(shù) h = 0p = 0.8931st = chi2stat: 1.6667 df: 5 edges:

12、 0.5000 1.5000 2.5000 3.5000 4.5000 5.5000 6.5000 O: 9 10 11 8 13 12 E: 10.5000 10.5000 10.5000 10.5000 10.5000 10.5000 講明：h=0(p值0.05)故同意原假設(shè)，認(rèn)為事故發(fā)生與星期幾無關(guān).Klomogorov-Smirnov檢驗(yàn) Klomogorov-Smirnov檢驗(yàn)是檢驗(yàn)任意已知分布函數(shù)的一種有效的假設(shè)檢驗(yàn)算法。MATLAB的統(tǒng)計(jì)學(xué)工具箱中提供了kstest函數(shù)實(shí)現(xiàn)該算法。其調(diào)用格式如下：h=kstest(X)h=kstest(X,CDF)h=kstest(X,CDF,alpha)h=kstest(X,CDF,alpha,type)h,p,ksstat,cv=kstest(.)例：clear all;X=-2:1:4h,p,k,c=kstest(X,0.05,0)XX=-3:.1:5;F=cdfplot(X);hold onG=plot(XX,norm