单个、双个正态分布区间估计--R code

代码是选修课《数据分析与统计》上附加题，可直接应用。欢迎纠错。

#*****************
#本程序利用R分布别做出单个、双个正态分布总体
#区间估计的均值和双侧、单侧置信区间
#包含4个函数
#code by Vac 2017.12.8
#*****************

#单个正态分布
#u的区间估计，sigma已知
onenorm_u_sigma<-function(X,sigma,alpha=0.99){
    n<-length(X);
    tmpx<-sigma*qnorm(1-alpha/2)/sqrt(n);
    a<-mean(X)-tmpx;b<-mean(X)+tmpx;#双侧
    cat("其",alpha*100,"%双侧置信区间是：[",a,",",b,"]","\n")

    bu<-mean(X)+sigma*qnorm(1-alpha)/sqrt(n)#单侧上限
    ad<-mean(X)-sigma*qnorm(1-alpha)/sqrt(n)#单侧下限
    cat("其",alpha*100,"%单侧置信区间上限是：",bu,"\n下限是",ad,"\n")
}

#u的区间估计，sigma未知
onenorm_u_sd<-function(X,alpha=0.99){
    n<-length(X);
    tmpx<-sd(X)*qt(1-alpha/2,n-1)/sqrt(n);
    a<-mean(X)-tmpx;b<-mean(X)+tmpx;#双侧
    cat("其",alpha*100,"%双侧置信区间是：[",a,",",b,"]","\n")

    bu<-mean(X)+sd(X)*qt(1-alpha,n-1)/sqrt(n)#单侧上限
    ad<-mean(X)-sd(X)*qt(1-alpha,n-1)/sqrt(n)#单侧下限
    cat("其",alpha*100,"%单侧置信区间上限是：",bu,"\n下限是",ad,"\n")
}

#sigma的区间估计，u已知
onenorm_sigma_u<-function(X,u,alpha=0.99){
    n<-length(X);
    a<-sum((X-u)^2)/qchisq(1-alpha/2,n);
    b<-sum((X-u)^2)/qchisq(alpha/2,n);#双侧
    cat("其",alpha*100,"%双侧置信区间是：[",a,",",b,"]","\n")

    bu<-sum((X-u)^2)/qchisq(alpha,n)#单侧上限
    ad<-sum((X-u)^2)/qchisq(1-alpha,n)#单侧下限
    cat("其",alpha*100,"%单侧置信区间上限是：",bu,"\n下限是",ad,"\n")
}

#sigma的区间估计，u未知
onenorm_sigma_sd<-function(X,alpha=0.99){
    n<-length(X);
    a<-(n-1)*sd(X)^2/qchisq(1-alpha/2,n-1);
    b<-(n-1)*sd(X)^2/qchisq(alpha/2,n-1);#双侧
    cat("其",alpha*100,"%双侧置信区间是：[",a,",",b,"]","\n")

    bu<-(n-1)*sd(X)^2/qchisq(alpha,n-1)#单侧上限
    ad<-(n-1)*sd(X)^2/qchisq(1-alpha,n-1)#单侧下限
    cat("其",alpha*100,"%单侧置信区间上限是：",bu,"\n下限是",ad,"\n")
}

##两个正态分布
#u1-u2的区间估计，sigma1,sigma2已知
twonorm_du_sigma<-function(X,Y,sigma1,sigma2,alpha=0.99){
    m<-length(X);
    n<-length(Y);
    tmp<-sqrt(sigma1^2/m+sigma2^2/n)*qnorm(1-alpha/2);
    a<-mean(X)-mean(Y)-tmp;
    b<-mean(X)-mean(Y)+tmp;#双侧
    cat("其",alpha*100,"%双侧置信区间是：[",a,",",b,"]","\n")

    bu<-mean(X)-mean(Y)+sqrt(sigma1^2/m+sigma2^2/n)*qnorm(1-alpha);#单侧上限
    ad<-mean(X)-mean(Y)-sqrt(sigma1^2/m+sigma2^2/n)*qnorm(1-alpha);#单侧下限
    cat("其",alpha*100,"%单侧置信区间上限是：",bu,"\n下限是",ad,"\n")
}

 #u1-u2的区间估计，sigma1,sigma2未知
twonorm_du_sd<-function(X,Y,alpha=0.99){
    m<-length(X);
    n<-length(Y);
    Sw<-sqrt((m-1)*sd(X)^2+(n-1)*sd(Y)^2)/(m+n-2);
    tmp<-Sw*sqrt(1/m+1/n)*qt(1-alpha/2,m+n-2);
    a<-mean(X)-mean(Y)-tmp;
    b<-mean(X)-mean(Y)+tmp;#双侧
    cat("其",alpha*100,"%双侧置信区间是：[",a,",",b,"]","\n")

    bu<-mean(X)-mean(Y)+Sw*sqrt(1/m+1/n)*qt(1-alpha,m+n-2);#单侧上限
    ad<-mean(X)-mean(Y)-Sw*sqrt(1/m+1/n)*qt(1-alpha,m+n-2);#单侧下限
    cat("其",alpha*100,"%单侧置信区间上限是：",bu,"\n下限是",ad,"\n")
}

 #sigma1^2/sigma2^2的区间估计，u1,u2已知
twonorm_sigma_u<-function(X,Y,u1,u2,alpha=0.99){
    m<-length(X);
    n<-length(Y);
    numerator<-n*sum((X-u1)^2)/m/sum((Y-u2)^2);
    a<-numerator/qf(1-alpha/2,m,n)
    b<-numerator/qf(alpha/2,m,n)#双侧
    cat("其",alpha*100,"%双侧置信区间是：[",a,",",b,"]","\n")

    bu<-numerator/qf(alpha,m,n)#单侧上限
    ad<-numerator/qf(1-alpha,m,n)#单侧下限
        cat("其",alpha*100,"%单侧置信区间上限是：",bu,"\n下限是",ad,"\n")
}

#sigma1^2/sigma2^2的区间估计，u1,u2未知
twonorm_sigma_sd<-function(X,Y,alpha=0.99){
    m<-length(X);
    n<-length(Y);
    numerator<-sd(X)^2/sd(Y)^2;
    a<-numerator/qf(1-alpha/2,m-1,n-1)
    b<-numerator/qf(alpha/2,m-1,n-1)#双侧
    cat("其",alpha*100,"%双侧置信区间是：[",a,",",b,"]","\n")

    bu<-numerator/qf(alpha,m-1,n-1)#单侧上限
    ad<-numerator/qf(1-alpha,m-1,n-1)#单侧下限
        cat("其",alpha*100,"%单侧置信区间上限是：",bu,"\n下限是",ad,"\n")
}