Question

Generate a data set from a normal distribution. Then you can apply bootstrap method to the generated data to obtain the empirical distribution of the coefficient of variation: sample standard deviation over sample mean, that is cv = s/¯ x. Describe this distribution. Also please describe the algorithm and attach the R code

Answer 1

We have done this problem in R

we have generated 500 samples from normal(0,1)

then we picked 2000 bootstrap from this and make the plot of CV as

The R code is

data=rnorm(500)
library(boot)
cv <- function( data, indices) {
d <- data[indices] # allows boot to select sample
fit <- sd(d)/mean(d)
return(fit)
}
# bootstrapping with 1000 replications
results <- boot(data=data, statistic=cv,
R=2000)
plot(results)

# the plot is

so the distribution CV concentrated at zero and it is symmetric, we can say that the distribution of CV is t-distribution but not normal since it has outliers