Unit4Homework/Bootstrap

Normal dist of sample 200 (Bootstrap)

y <- rnorm(200, 20, 5)
n <-1000  # Simple normal distribution
tdata <- numeric(n)
for(i in 1:n) {
    samp <- sample(y, 200, replace=TRUE)
    tdata [i] <- mean(samp)
}
summary(tdata)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   19.01   19.89   20.10   20.11   20.32   21.31

hist(tdata)

##Normal distribution of size 100

x <- rnorm(100, 20, 5)
bar <- mean(x)
normdata <- numeric(2000)  ## Find the pivot t-interval
for (i in 1:2000){
    samp <- sample(y,size=70,replace=TRUE)
    bootmean = mean(samp)
    bootsd = sd(samp)
    tpivot = (bootmean - bar)/(bootsd/sqrt(100))
    normdata[i] <- tpivot
}
quantile <- quantile(normdata, c(0.025, 0.975)) # numbers at 2.5% and 97.5% quantile 
quantile

##      2.5%     97.5% 
## -2.768695  1.826441

Exponential distribution: sample size 30

n <- 30 
exp <- numeric(2000)

for (i in 1:2000){
    x <- exp(n)
    exp[i] <- mean(x)
}
mean(exp)

## [1] 1.068647e+13

Exponential distribution: sample size 80

n <- 80 
exp <- numeric(2000)
for (i in 1:2000){
    x <- exp(n)
    exp[i] <- mean(x)
}
mean(exp)

## [1] 5.540622e+34