I have calculated probability distributions of a product’s consumption for males and females in a single member household. Next, I would like to apply those distributions to households that contain more than one member for e.g. household occupied by one male and two females or one male and one female. How can I code in stan to merge two or more probability distributions such that, the sum is less than total amount bought by the household.

My data looks like:

Household Member3 Gender1 Gender2 Gender3 ProbDist1 ProbDist2 ProbDist3 TotalAmountBought

1 3 Male Male Female N(3.2,0.3) N(3.2,0.3) N(2.1,0.5) 4

2 2 Male Male N(3.2,0.3) N(3.2,0.3) 2

3 2 Male Female N(3.2,0.3) N(2.1,0.5) 3

My upper limit of summing the probability distributions is defined by the TotalAmountBought.