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Higher order moments

  1. Sep 9, 2009 #1
    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. jcsd
  3. Sep 9, 2009 #2
    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.
  4. Sep 9, 2009 #3


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    Homework Helper

    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?
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