Best way to simulate an inverse?

[John Shannon]

I need to simulate the inverse of a function that has no closed-form solution, and I was wondering if there's a clean way to do that in Stata. So far I've been doing something along the lines of:

set obs 1000
gen x = _n
gen y = expression in terms of x

and then just matching values of y to values in my data, which is not at all practical for large datasets. I know Stata can graph continuous functions using twoway function, but is there a way to exploit this ability to back out values of x from a given value of the function?

[Nick Cox]

This sounds like a case for interpolating x as a function of y. In practice, I would often use cubic splines. mipolate (SSC) is a wrapper for the inbuilt Mata functions.

[Maarten Buis]

You can go more fancy by choosing where to place the knots in some close to optimal manner. I did that with some Mata code in margdistfit. The source code is available on SSC as ancillary files.