
R Assignment Solution on Distribution
- 10th Nov, 2021
- 15:41 PM
M=1000 n=c(10,30,100) normal_est=function(n){ data=rnorm(n,0,1) output=c(mean(data),median(data),mean(max(data),min(data)),IQR(data)) return(output) } unif_est=function(n){ data=runif(n,0,1) output=c(mean(data),median(data),mean(max(data),min(data)),IQR(data)) return(output) } exp_est=function(n){ data=rexp(n,1) output=c(mean(data),median(data),mean(max(data),min(data)),IQR(data)) return(output) } norm_stat1=data.frame() unif_stat1=data.frame() exp_stat1=data.frame() norm_stat2=data.frame() unif_stat2=data.frame() exp_stat2=data.frame() norm_stat3=data.frame() unif_stat3=data.frame() exp_stat3=data.frame() for(i in 1:M){ norm_stat1=rbind(norm_stat1,normal_est(n[1])) unif_stat1=rbind(unif_stat1,unif_est(n[1])) exp_stat1=rbind(exp_stat1,exp_est(n[1])) norm_stat2=rbind(norm_stat2,normal_est(n[2])) unif_stat2=rbind(unif_stat2,unif_est(n[2])) exp_stat2=rbind(exp_stat2,exp_est(n[2])) norm_stat3=rbind(norm_stat3,normal_est(n[3])) unif_stat3=rbind(unif_stat3,unif_est(n[3])) exp_stat3=rbind(exp_stat3,exp_est(n[3])) } colnames(norm_stat1)=c("mean","median","midrange","midquartile") colnames(norm_stat2)=c("mean","median","midrange","midquartile") colnames(norm_stat3)=c("mean","median","midrange","midquartile") colnames(unif_stat1)=c("mean","median","midrange","midquartile") colnames(unif_stat2)=c("mean","median","midrange","midquartile") colnames(unif_stat3)=c("mean","median","midrange","midquartile") colnames(exp_stat1)=c("mean","median","midrange","midquartile") colnames(exp_stat2)=c("mean","median","midrange","midquartile") colnames(exp_stat3)=c("mean","median","midrange","midquartile") #normal ##10 plot(density(norm_stat1$mean),xlim=c(-1.5,4),ylim=c(0,1.2)) lines(density(norm_stat1$median),col='red') lines(density(norm_stat1$midrange),col='blue') lines(density(norm_stat1$midquartile),col='green') par(mfrow=c(1,4)) boxplot(norm_stat1$mean,main="mean") boxplot(norm_stat1$median,main="median") boxplot(norm_stat1$midrange,main="midrange") boxplot(norm_stat1$midquartile,main="midquartile") pairs(norm_stat1) ##30 plot(density(norm_stat2$mean),xlim=c(-1.5,4),ylim=c(0,2)) lines(density(norm_stat2$median),col='red') lines(density(norm_stat2$midrange),col='blue') lines(density(norm_stat2$midquartile),col='green') par(mfrow=c(1,4)) boxplot(norm_stat2$mean,main="mean") boxplot(norm_stat2$median,main="median") boxplot(norm_stat2$midrange,main="midrange") boxplot(norm_stat2$midquartile,main="midquartile") pairs(norm_stat2) ##100 plot(density(norm_stat3$mean),xlim=c(-1.5,4),ylim=c(0,4)) lines(density(norm_stat3$median),col='red') lines(density(norm_stat3$midrange),col='blue') lines(density(norm_stat3$midquartile),col='green') par(mfrow=c(1,4)) boxplot(norm_stat3$mean,main="mean") boxplot(norm_stat3$median,main="median") boxplot(norm_stat3$midrange,main="midrange") boxplot(norm_stat3$midquartile,main="midquartile") pairs(norm_stat3) #unif ##10 plot(density(unif_stat1$mean),xlim=c(-0.1,1.5),ylim=c(0,7)) lines(density(unif_stat1$median),col='red') lines(density(unif_stat1$midrange),col='blue') lines(density(unif_stat1$midquartile),col='green') par(mfrow=c(1,4)) boxplot(unif_stat1$mean,main="mean") boxplot(unif_stat1$median,main="median") boxplot(unif_stat1$midrange,main="midrange") boxplot(unif_stat1$midquartile,main="midquartile") pairs(unif_stat1) ##30 plot(density(unif_stat2$mean),xlim=c(-0.1,1.5),ylim=c(0,21)) lines(density(unif_stat2$median),col='red') lines(density(unif_stat2$midrange),col='blue') lines(density(unif_stat2$midquartile),col='green') par(mfrow=c(1,4)) boxplot(unif_stat2$mean,main="mean") boxplot(unif_stat2$median,main="median") boxplot(unif_stat2$midrange,main="midrange") boxplot(unif_stat2$midquartile,main="midquartile") pairs(unif_stat2) ##100 plot(density(unif_stat3$mean),xlim=c(-0.1,1.5),ylim=c(0,40)) lines(density(unif_stat3$median),col='red') lines(density(unif_stat3$midrange),col='blue') lines(density(unif_stat3$midquartile),col='green') par(mfrow=c(1,4)) boxplot(unif_stat3$mean,main="mean") boxplot(unif_stat3$median,main="median") boxplot(unif_stat3$midrange,main="midrange") boxplot(unif_stat3$midquartile,main="midquartile") pairs(unif_stat3) #exp ##10 plot(density(exp_stat1$mean),xlim=c(-0.1,5),ylim=c(0,2)) lines(density(exp_stat1$median),col='red') lines(density(exp_stat1$midrange),col='blue') lines(density(exp_stat1$midquartile),col='green') par(mfrow=c(1,4)) boxplot(exp_stat1$mean,main="mean") boxplot(exp_stat1$median,main="median") boxplot(exp_stat1$midrange,main="midrange") boxplot(exp_stat1$midquartile,main="midquartile") pairs(exp_stat1) ##30 plot(density(exp_stat2$mean),xlim=c(-0.1,5),ylim=c(0,2)) lines(density(exp_stat2$median),col='red') lines(density(exp_stat2$midrange),col='blue') lines(density(exp_stat2$midquartile),col='green') par(mfrow=c(1,4)) boxplot(exp_stat2$mean,main="mean") boxplot(exp_stat2$median,main="median") boxplot(exp_stat2$midrange,main="midrange") boxplot(exp_stat2$midquartile,main="midquartile") pairs(exp_stat2) ##100 plot(density(exp_stat3$mean),xlim=c(-0.1,10),ylim=c(0,4)) lines(density(exp_stat3$median),col='red') lines(density(exp_stat3$midrange),col='blue') lines(density(exp_stat3$midquartile),col='green') par(mfrow=c(1,4)) boxplot(exp_stat3$mean,main="mean") boxplot(exp_stat3$median,main="median") boxplot(exp_stat3$midrange,main="midrange") boxplot(exp_stat3$midquartile,main="midquartile") pairs(exp_stat3) mean(norm_stat1$mean) mean(norm_stat1$median) mean(norm_stat1$midrange) mean(norm_stat1$midquartile) sd(norm_stat1$mean) sd(norm_stat1$median) sd(norm_stat1$midrange) sd(norm_stat1$midquartile) mean(norm_stat2$mean) mean(norm_stat2$median) mean(norm_stat2$midrange) mean(norm_stat2$midquartile) sd(norm_stat2$mean) sd(norm_stat2$median) sd(norm_stat2$midrange) sd(norm_stat2$midquartile) mean(norm_stat3$mean) mean(norm_stat3$median) mean(norm_stat3$midrange) mean(norm_stat3$midquartile) sd(norm_stat3$mean) sd(norm_stat3$median) sd(norm_stat3$midrange) sd(norm_stat3$midquartile) mean(unif_stat1$mean) mean(unif_stat1$median) mean(unif_stat1$midrange) mean(unif_stat1$midquartile) sd(unif_stat1$mean) sd(unif_stat1$median) sd(unif_stat1$midrange) sd(unif_stat1$midquartile) mean(unif_stat2$mean) mean(unif_stat2$median) mean(unif_stat2$midrange) mean(unif_stat2$midquartile) sd(unif_stat2$mean) sd(unif_stat2$median) sd(unif_stat2$midrange) sd(unif_stat2$midquartile) mean(unif_stat3$mean) mean(unif_stat3$median) mean(unif_stat3$midrange) mean(unif_stat3$midquartile) sd(unif_stat3$mean) sd(unif_stat3$median) sd(unif_stat3$midrange) sd(unif_stat3$midquartile) mean(exp_stat1$mean) mean(exp_stat1$median) mean(exp_stat1$midrange) mean(exp_stat1$midquartile) sd(exp_stat1$mean) sd(exp_stat1$median) sd(exp_stat1$midrange) sd(exp_stat1$midquartile) mean(exp_stat2$mean) mean(exp_stat2$median) mean(exp_stat2$midrange) mean(exp_stat2$midquartile) sd(exp_stat2$mean) sd(exp_stat2$median) sd(exp_stat2$midrange) sd(exp_stat2$midquartile) mean(exp_stat3$mean) mean(exp_stat3$median) mean(exp_stat3$midrange) mean(exp_stat3$midquartile) sd(exp_stat3$mean) sd(exp_stat3$median) sd(exp_stat3$midrange) sd(exp_stat3$midquartile) ##question 3 library(MASS) library(boot) data=Cars93 cv=function(x,n){sd(x[n])/mean(x[n])} B=boot(data$EngineSize,cv,1000) boot.ci(B) #t -ci upper2=mean(B$t)+sd(B$t)*qt(0.95,999) lower2=mean(B$t)+sd(B$t)*qt(0.05,999) #permutation test library(coin) independence_test(EngineSize~Origin,data=data)