If I have a mixture distribution with two normal components like so

wN(\mu_1, \sigma^2_1) + (1 - w)N(\mu_2, \sigma^2_2)

it is relatively simple to calculate the pdf and the cdf of this distribution. I know that the cdf is

F(x) = wF_1(x) + (1-w)F_2(x)

I would like to calculate the inverse cdf F^{-1}(x). I’m able to do this in R using the `uniroot`

or the `optim`

function, but how would I go about doing this in stan?