#examples of using the function sample

#permutation of seq 1-10
sample(10)

#resample from seq 1-10
sample(10, replace=T)

#resampling from 1-10 
#probabilities favor numbers 1-5
prob1 <- c(rep(.15, 5), rep(.05, 5))
prob1
sample(10, replace=T, prob=prob1)

#sample of size 5 from elements of a matrix 
y1 <- matrix( round(rnorm(25,5)), ncol=5)
y1

x1 <- y1[sample(25, 5)]
x1

#sampling the rows of the a matrix
y2 <- matrix( round(rnorm(40, 5)), ncol=5)
y2

x2 <- y2[sample(8, 3), ]
x2

#bootstrap the standard error of the median
data <- round(rnorm(100, 5, 5))
data[1:10]
resamples <- lapply(1:20, function(i) sample(data, replace=T))
resamples[1]
r.median <- sapply(resamples, median)
r.median
sqrt(var(r.median))
windows(5,5)
hist(r.median)

#function which will bootstrap the standard error of the median
b.median <- function(data, num) {
   resamples <- lapply(1:20, function(i) sample(data, replace=T))
   r.median <- sapply(resamples, median)
   std.err <- sqrt(var(r.median))
   list(std.err=std.err, resamples=resamples, medians=r.median)   
}

data1 <- round(rnorm(100, 5, 5))
b1 <- b.median(data1, 30)
b1$resamples[1]
b1$std.err
windows(5,5)
hist(b1$medians)

b.median(rnorm(100, 5, 2), 50)$std.err

#making the function more general
#can use any summary statistic not just median
b.stat <- function(data, num, stat) {
    resamples <- lapply(1:20, function(i) sample(data, replace=T))
    r.stat <- sapply(resamples, stat)
    std.err <- sqrt(var(r.stat))
    list(std.err=std.err, resamples=resamples, stats=r.stat)   
}

b.stat(rnorm(100, 5, 2), 50, var)$std.err
windows(5,5)
hist(b.stat(rnorm(100, 5, 2), 50, var)$stats)

data(city)
ratio <- function(d, w) sum(d$x * w)/sum(d$u * w)
boot(city, ratio, R=999, stype="w")