MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Hello I'm sorry if this question is trivial but I haven't been able to find an answer. I'm trying to show that a sequence of distributions on $\mathbb{R}^n$ converges to the normal distribution by showing that the moments of the distributions converge to those of the normal distribution. Is this sufficient under appropriate assumptions? Thanks

share|cite|improve this question
up vote 1 down vote accepted

Yes, without any additional assumptions — the relevant technical conditions are satisfied because your limit distribution is normal. For sufficiency in the univariate case, see any probability textbook that covers the method of moments, for example section 30 of Billingsley's Probability and Measure. The multivariate case follows from the univariate case by the Cramér–Wold device, see for example section 29 of Billingsley.

share|cite|improve this answer
Also, as for whether the question is trivial, it's easy and well-known folklore, but it's surprisingly hard to find written down. – Mark Meckes Dec 13 '12 at 17:35
Thanks a lot! It's nice not to be working towards a dead end:-) – NA007 Dec 13 '12 at 18:51

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.