参数估计与假设检验.pptx

天津科技大学数学系谢中华E-mail:xiezhhMATLAB从零到进阶,参数估计与假设检验,主要内容常见分布的参数估计正态总体参数的检验,第二节常见分布的参数估计,一、分布参数估计的MATLAB函数,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).*(x0phat,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】调用normrnd函数生成100个服从均值为10，标准差为4的正态分布的随机数，然后调用mle函数求均值和标准差的最大似然估计。,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,.),补充：mle函数的调用格式：,第三节正态总体参数的检验,一、总体标准差已知时的单个正态总体均值的U检验,调用格式：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函数,x=9710210511299103102941009510598102100103;h,p,muci,zval=ztest(x,100,2,0.05)h,p,muci,zval=ztest(x,100,2,0.05,right),二、总体标准差未知时的单个正态总体均值的t检验,调用格式：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函数,x=49.450.550.751.749.847.949.251.448.9;h,p,muci,stats=ttest(x,50,0.05),三、总体标准差未知时的两个正态总体均值的比较t检验,调用格式：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函数,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、总体均值未知时的单个正态总体方差的卡方检验,调用格式：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函数,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、总体均值未知时的两个正态总体方差的比较F检验,调用格式：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函数,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),