I can't fit X to a common distribution so currently I just have X ~ ecdf(sample_data).
How do I calculate the empirical distribution of sum(X1 + ... + Xn), given n? X1 to Xn are iid.
My sample size is around $6\times10^7$. $n$ needs to be around 10-20.
To give an example of what I am doing: Suppose X is the age of a person. If I put 10-20 people in a room, what is the distribution of the sum of ges in the room? I have lots of peoples ages, and no reason to fit the distribution of an age to any of the common distributions.
(previously on StackOverflow - suggested to move here).