sd_sk: Calculate the standard error of q sample quantile using exact...
In XixuHu/SC19090: Statistical Computing Final Project, 2019 FALL, USTC

Description Usage Arguments Details Value Examples

Calculate the standard error of q sample quantile using exact variance formula of skewness

1	sd_sk(x, q, n)

`x`	the quantiles of skewness coefficient
`q`	quantiles
`n`	number of samples

The variance of q sample quantile of skewness is Var(hat(x[q]))=frac(q(1-q),nf^2*(x)) where f is the density of the sampled distribution. Using the normal approximation for the density, the skewness is asymptotically normal with mean 0 and variance frac(6(n-2),(n+1)(n+3))

the standard error of q sample quantile of skewness coefficient

## Not run: 
 m=1000;n=100
 stat = replicate(m, expr={
 x = rnorm(n)
 y = sk(x)
 })
 q = c(.025,.05,.95,.975)
 x = quantile(stat,q)
 print('The standard error of the estimates:');sd_sk(x,q,n)

## End(Not run)