So, I'm working on a problem where I have a sample distribution with a reported, mean and an asymmetric confidence interval from bootstrapped sampling of the initial population (this is from a meta-analysis - so, I also have the # of bootstrap replicates and the original sample size). Given this information, I would like to draw a random variable (I'm then going use it to construct my own bootstrapped sample using other similar variables - basically, a meta-analysis of meta-analyses). I'm sure this is simple, but I'm completely blanking on how one would do this - is there an appropriate distribution to draw from or way to back-engineer reported results to create one? R code would be great (if there is a package to do this), or just a see-this-reference, as I'm drawing a blank.
N.B. I think my larger question here was, if you have the quantiles for a population, but no other distributional knowledge or data, is it possible to create a method to draw random numbers based on that information. But perhaps the answer there is no.