Talk:Moment closure

Accuracy

Is there a better general statement of this. It can't literally be "the moments" being set to zero ... it might be the cumulants, which would work for the normal distribution approximations mentioned, and one of reference titles mentions cumulants. Or there may be some other way of specifying higher moments from lower moments. Anyone have access to the sources quoted? Melcombe (talk) 23:09, 3 May 2012 (UTC)[reply]

You're right. "The estimates for the mean and variance were obtained by setting

\mu _{3}(t)=3\mu _{2}(t)\mu _{1}(t)-2\mu _{1}(t)^{3}

that is, the normal approximation that corresponds to setting cumulants of order 3 and above to be 0."^ref I'll try to clarify this in the article. Gareth Jones (talk) 16:16, 25 May 2012 (UTC)[reply]

That leaves the question of whether the method has ever been attempted for cumulants of order n or more set to zero, with n grater than 3 ... given that if the third cumulant is non-zero, all the higher cumulants cannot be equal to zero. Notionally the attempt must either fail or give a result correponding to a density function that is not a proper probability density function. The higher order limit is implied in the present laed section. Melcombe (talk) 00:38, 28 May 2012 (UTC)[reply]