Most asymptotic results in statistics prove that as n \rightarrow \infty an estimator (such as the MLE) converges to a normal distribution based on a second-order taylor expansion of the likelihood function. I believe there’s a similar result in Bayesian literature, the “Bayesian Central Limit Theorem”, which shows that the posterior converges asymptotically to a normal as n \rightarrow \infty

My question is – does the distribution converge to something “before” it becomes normal, based on the third term in the Taylor series? Or is this not possible to do in general?

**Answer**

You are searching for the Edgeworth series aren’t you?

http://en.wikipedia.org/wiki/Edgeworth_series#Edgeworth_series

(note that Edgeworth died in 1926, should be in most famous statisticians? )

**Attribution***Source : Link , Question Author : gabgoh , Answer Author : robin girard*