In article <1103_987867120@byu-b51twg54m4e>,
David J. <[EMAIL PROTECTED]> wrote:
>I am trying to get a better understanding of the proof for the central limit theorem
>which uses the MGF. Can anyone direct me to some resources that will lead me through
>this
>proof step by step? Thanks.
>Dave J.
Essentially what you are asking for is trivial, if
you accept the theorems that the moment generating
function determines the distribution, and that
convergence of the moment generating function is
equivalent to convergence of the distributions.
This is usually done by using the characteristic
function instead. The advantage of this is that
the characteristic function always exists, while
the moment generating function does not, and the
complex variable proofs for the characteristic
function are easier than the proofs for the moment
generating function. It gets down to the essential
conditions, which are much weaker than the existence
of a moment generating function.
Any good book on probability using measure theory
is likely to have the necessary proofs.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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