If you have a parameter that is dependent on multiple predictor variables, there are standard statistical techniques that you can use to establish their relationship. From your question, it is unclear what the parameter is, whose statistical distribution you are interested in.
See books like this: https://www.amazon.com/Ewout-Steyerberg-Prediction-Development-Validation/dp/B005MH99GW/ref=sr_1_3?crid=16C4G2T47ISCZ&keywords=ewout+steyerberg&qid=1583094983&sprefix=ewout%2Caps%2C263&sr=8-3