# Sum of N random variables from the same distributions [duplicate]

Given $$n$$ independent random variables from the same distribution, how to obtain the distribution of their sum? For example, the distribution of $$n$$ normal distribution is $$N(n\mu, n\delta^2)$$. Similarly, the sum of exponential distribution is gamma distribution.

Is there any possible way to obtain the distribution of their sum? For example, the sum of $$n$$ Pareto distribution.

• You can't compute the distribution of the sum unless you have their joint distribution. Just knowing the marginal distributions is not sufficient. Mar 3, 2019 at 4:05
• For Pareto, maybe look here. Also google; there are some links that aren't behind pay-walls---especially if you go beyond the first 'commercial' pages. Mar 3, 2019 at 4:34
• More generally, assuming the distributions are independent, you might take the product of their moment generating functions (MGFs) and see if you can recognize the result as the MGF belonging to some known distribution. For many families of distributions, Wikipedia shows MGFs. (Some distn's don't have an MGF, then you might use characteristic functions, if you know about them.) Mar 3, 2019 at 4:38