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天津科技大學(xué)數(shù)學(xué)系謝中華E-mail:xiezhh@MATLAB從零到進階,參數(shù)估計與假設(shè)檢驗,主要內(nèi)容常見分布的參數(shù)估計正態(tài)總體參數(shù)的檢驗,第二節(jié)常見分布的參數(shù)估計,一、分布參數(shù)估計的MATLAB函數(shù),>>x=[15.14,14.81,15.11,15.26,15.08,15.17,15.12,14.95,15.05,14.87];>>[muhat,sigmahat,muci,sigmaci]=normfit(x,0.1)>>[mu_sigma,mu_sigma_ci]=mle(x,distribution,norm,alpha,0.1),>>x=[0.7917,0.8448,0.9802,0.8481,0.76270.9013,0.9037,0.7399,0.7843,0.84240.9842,0.7134,0.9959,0.6444,0.83620.7651,0.9341,0.6515,0.7956,0.8733];>>PdfFun=@(x,theta)theta*x.^(theta-1).*(x>0>>[phat,pci]=mle(x(:),pdf,PdfFun,start,1),>>x=normrnd(10,4,100,1);>>[phat,pci]=mle(x)>>[phat,pci]=mle(x,distribution,normal)>>[phat,pci]=mle(x,pdf,@normpdf,start,[0,1])>>[phat,pci]=mle(x,cdf,@normcdf,start,[0,1]),【例18.2-3】調(diào)用normrnd函數(shù)生成100個服從均值為10，標準差為4的正態(tài)分布的隨機數(shù)，然后調(diào)用mle函數(shù)求均值和標準差的最大似然估計。,phat=mle(data)[phat,pci]=mle(data)[...]=mle(data,distribution,dist)[...]=mle(data,...,name1,val1,name2,val2,...)[...]=mle(data,pdf,pdf,cdf,cdf,start,start,...)[...]=mle(data,logpdf,logpdf,logsf,logsf,start,start,...)[...]=mle(data,nloglf,nloglf,start,start,...),補充：mle函數(shù)的調(diào)用格式：,第三節(jié)正態(tài)總體參數(shù)的檢驗,一、總體標準差已知時的單個正態(tài)總體均值的U檢驗,調(diào)用格式：h=ztest(x,m,sigma)h=ztest(...,alpha)h=ztest(...,alpha,tail)h=ztest(...,alpha,tail,dim)[h,p]=ztest(...)[h,p,ci]=ztest(...)[h,p,ci,zval]=ztest(...),ztest函數(shù),>>x=[9710210511299103102941009510598102100103];>>[h,p,muci,zval]=ztest(x,100,2,0.05)>>[h,p,muci,zval]=ztest(x,100,2,0.05,right),二、總體標準差未知時的單個正態(tài)總體均值的t檢驗,調(diào)用格式：h=ttest(x)h=ttest(x,m)h=ttest(x,y)h=ttest(...,alpha)h=ttest(...,alpha,tail)h=ttest(...,alpha,tail,dim)[h,p]=ttest(...)[h,p,ci]=ttest(...)[h,p,ci,stats]=ttest(...),ttest函數(shù),>>x=[49.450.550.751.749.847.949.251.448.9];>>[h,p,muci,stats]=ttest(x,50,0.05),三、總體標準差未知時的兩個正態(tài)總體均值的比較t檢驗,調(diào)用格式：h=ttest2(x,y)h=ttest2(x,y,alpha)h=ttest2(x,y,alpha,tail)h=ttest2(x,y,alpha,tail,vartype)h=ttest2(x,y,alpha,tail,vartype,dim)[h,p]=ttest2(...)[h,p,ci]=ttest2(...)[h,p,ci,stats]=ttest2(...),ttest2函數(shù),>>x=[20.1,20.0,19.3,20.6,20.2,19.9,20.0,19.9,19.1,19.9];>>y=[18.6,19.1,20.0,20.0,20.0,19.7,19.9,19.6,20.2];>>alpha=0.05;>>tail=both;>>vartype=equal;>>[h,p,muci,stats]=ttest2(x,y,alpha,tail,vartype),四、總體均值未知時的單個正態(tài)總體方差的卡方檢驗,調(diào)用格式：H=vartest(X,V)H=vartest(X,V,alpha)H=vartest(X,V,alpha,tail)[H,P]=vartest(...)[H,P,CI]=vartest(...)[H,P,CI,STATS]=vartest(...)[...]=vartest(X,V,alpha,tail,dim),vartest函數(shù),>>x=[49.450.550.751.749.847.949.251.448.9];>>var0=1.5;>>alpha=0.05;>>tail=both;>>[h,p,varci,stats]=vartest(x,var0,alpha,tail),五、總體均值未知時的兩個正態(tài)總體方差的比較F檢驗,調(diào)用格式：H=vartest2(X,Y)H=vartest2(X,Y,alpha)H=vartest2(X,Y,alpha,tail)[H,P]=vartest2(...)[H,P,CI]=vartest2(...)[H,P,CI,STATS]=vartest2(...)[...]=vartest2(X,Y,alpha,tail,dim),vartest2函數(shù),>>x=[20.1,20.0,19.3,20.6,20.2,19.9,20.0,19.9,19.1,19.9];>>y=[18.6,19.1,20.0,20.0,20.0,19.7,19.9,19.6,20.2];>>alpha=0.05;>>tail=both;>>[h,p,varci,stats]=vartest2(x,y,alpha,tail),