Math312_project2.Rmd

---
title: "312_Project_2"
author: "Kenneth Cho, Thomas Liu, and Andrew MacCausland"
date: "11/21/2021"
output: pdf_document
---

```{r}
library('boot')
```


```{r}
# this function will return the ci object for 1 sample
get_ci <- function(){
  # generate 20 samples from standard normal
  stdnormal <- rnorm(20)
  # calculate the ci object
  boot.obj <- boot(stdnormal, R=2000, statistic=function(x, i){mean(x[i])})
} 
```


```{r}
set.seed(1331)
norm_miss <- 0
basic_miss <- 0
perc_miss <- 0
# calculate coverage rate, run 1000 times
for (i in 1:1000){
  boot.obj = get_ci()
  intervals <- boot.ci(boot.obj, type = c("norm", "basic", "perc"))
  norm_min <- intervals$normal[2]
  norm_max <- intervals$normal[3]
  basic_min <- intervals$basic[4]
  basic_max <- intervals$basic[5]
  perc_min <- intervals$percent[4]
  perc_max <- intervals$percent[5]
  
  # get misses
  if(0 < norm_min | 0 > norm_max){
    norm_miss <- norm_miss + 1
  }
  if(0 < basic_min | 0 > basic_max){
    basic_miss <- basic_miss + 1
  }
  if(0 < perc_min | 0 > perc_max){
    perc_miss <- perc_miss + 1
  }
}
cat("coverage rate for standard normal ci: ", 100 - norm_miss / 10, "%\n")
cat("coverage rate for basic ci: ", 100 - basic_miss / 10, "%\n")
cat("coverage rate for percentile ci: ", 100 - perc_miss / 10, "%\n")

```

```{r}
# modify the loop above a bit to get the proportions of times that the 
# confidence intervals miss on the left, and the proportion of times
# that the confidence intervals miss on the right
norm_miss_L <- 0
basic_miss_L <- 0
perc_miss_L <- 0
norm_miss_R <- 0
basic_miss_R <- 0
perc_miss_R <- 0
set.seed(1331)
# calculate coverage rate, run 1000 times
for (i in 1:1000){
  boot.obj = get_ci()
  intervals <- boot.ci(boot.obj, type = c("norm", "basic", "perc"))
  norm_min <- intervals$normal[2]
  norm_max <- intervals$normal[3]
  basic_min <- intervals$basic[4]
  basic_max <- intervals$basic[5]
  perc_min <- intervals$percent[4]
  perc_max <- intervals$percent[5]
  
  # get misses
  if(0 < norm_min){
    norm_miss_L <- norm_miss_L + 1
  }
  if(0 < basic_min){
    basic_miss_L <- basic_miss_L + 1
  }
  if(0 < perc_min){
    perc_miss_L <- perc_miss_L + 1
  }
  if(0 > norm_max){
    norm_miss_R <- norm_miss_R + 1
  }
  if(0 > basic_max){
    basic_miss_R <- basic_miss_R + 1
  }
  if(0 > perc_max){
    perc_miss_R <- perc_miss_R + 1
  }
}
print("normal")
print(norm_miss_L)
print(norm_miss_R)

print("basic")
print(basic_miss_L)
print(basic_miss_R)

print("perc")
print(perc_miss_L)
print(perc_miss_R)
```