I am tasked with developing confidence intervals for the function x = 1 - |(a+b)/c| where a, b and c are random variables. a and b are normally distributed, but c is heavily skewed left. further there b and c are correlated (Pearson = .21). x belongs to [-inf, 1] and is skewed left because of its domain. I have 2000 "rows" of data.
I can't see an analytic solution for this equation/problem. I was thinking this would be a great opportunity to bootstrap an estimate. I've approached it two ways; 1) resample a, b, and c independently. Then, calculate x^ each time, then take summary statistics for every iteration. Iterate 10,000 or so times. 2) resample the rows of data for a, b, and c. Calculate x^ and take summary statistics. Again, iterate 10,000 or so times.
I think the correct approach is 2 because then the correlation between b and c will be present in the data. Please tell me if I'm right.
Now once if have a big collection of means of x^ can I use the standard deviation of the means of x^ to get the 95% or whatever % confidence bounds?