# Higher order moments

1. Sep 9, 2009

### benjaminmar8

Hi, all,

Let's assume a random variable's variance is zero as sample size tends to infinity somehow, can I say that its higher order central moments are also zero as the sample size tends to infinity?

Thks a lot

2. Sep 9, 2009

### John Creighto

That makes sense to me given that when the variance gets very small the higher order central moments should tend to zero faster then the variance because the square of a small quantity is even smaller then that small quantity.

3. Sep 9, 2009

Your question really doesn't make sense: a random variable has a single distribution (normal distribution, chi-square distribution, etc) and does not depend on a sample size. if you respond "t-distribution" - that doesn't fit your comment: t-distributions are INDEXED by their degrees of freedom, but there is no requirement that there be a link to sample size.

do you mean this:
if, in a series of samples of increasing sample size, if the sample variance tends to zero then all higher-order moments tend to zero?

or do you mean this:

if a (degenerate) distribution has variance zero, are all higher-order moments equal to zero.

One other possibility: are you talking about the behavior of SAMPLING distributions as the sample size tends to infinity?