For some analysis I have two input variables with some (unknown) probabilities distributions. Of both the input variables I know the (assumed) 10th, 50th and 90th percentile. I have some simple model based on (deterministic) logic that translates these two inputs to an output that I am interested in.
My question now: considering I use the 10th percentiles of those two input variables, and run these values through my model. Is my output now also the 10th percentile of its own probability distribution (which is a combination of the two distributions of the inputs I think)?
Above I wrote that the probability distribution of my input variables are unknown, which I could imagine makes it impossible to know what the percentile of the output variable is. Therefore I was wondering if it would be possible to determine the percentile of the output if we assume the inputs are normally distributed?
My current thought: it is impossible to determine this analytically (even in the case of assumed normality of the inputs), and it could be useful to apply simulation. That is, generate a thousand samples from the probability distributions of the two inputs (assuming they are independent) and run those samples through the model in order to find the approximated 10th percentile from the probability distribution of my output variable.
Let me know if anything is unclear, thanks for your thoughts!