Simulation for Confidence interval in R

Question

I have an R function that provides the 95% confidence Interval for the ncp (non-centrality parameter) of at distribution.

Via simulation in R, is it possible to show that in the long-run the CIs from this R function capture a given TRUE ncp (here "2" same as input t ) 95% of the time?

(I appreciate any ideas as to how to do this)

CI.ncp <- function(t, N){

  f <- function (ncp, alpha, q, df) {  
abs(suppressWarnings(pt(q = t, df = N - 1, ncp, lower.tail = FALSE)) - alpha) }

sapply(c(0.025, 0.975),
function(x) optim(1, f, alpha = x, q = t, df = N - 1, control = list(reltol = (.Machine$double.eps)))[[1]]) }

#Example of Use:
CI.ncp(t = 2, N = 20) # gives: -0.08293755  4.03548862 

#(in the long-run 95% of the time, "2" is contained within these
# two numbers, how to show this in R?)

Here is what I have tried with no success:

fun <- function(t = 2, N = 20){

  ncp = rt(1, N - 1, t)
  CI.ncp(t = 2, N = 20)
  mean(ncp <= 2 & 2 <= ncp )
   }

 R <- 1000
 sim <- t(replicate(R, fun()))
 coverage <- mean(sim[,1] <= 2 & 2 <= sim[,2])

Answer 1

The problem is the that we need to feed the random ncp obtained from the fun in the CI.ncp :

 fun <- function(t = 2, N = 20){ ;

   ncp = rt(1, N - 1, t);
   CI.ncp(t = ncp, N = 20);
   }

  R <- 1e4 ;
  sim <- t(replicate(R, fun()));
  coverage <- mean(sim[,1] <= 2 & 2 <= sim[,2])

Answer 2

I would use package MBESS .

#install.packages("MBESS")
library(MBESS)

fun <- function(t = 2, N = 20, alpha = 0.95){
   x = rt(1, N - 1, t)
   conf.limits.nct(x, df = N, conf.level = alpha)[c(1, 3)]
}

set.seed(5221)
R <- 1000
sim <- t(replicate(R, fun()))
head(sim)
coverage <- mean(sim[,1] <= 2 & 2 <= sim[,2])
coverage
[1] 0.941