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 | | From: | Yan ZHANG | | Subject: | same entropy between two probability distribution functions. | | Date: | Fri, 21 Jan 2005 00:43:16 +0800 |
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 | Suppose that a non-negative random variable X follows probability density
function f_X(t). Since f_X(t) is too complicated, I would like to
approximate f_X(t) by simpler function f_X2(t) such as exponential or
hyper-exponential distribution.
I was once suggested that f_X(t) can be approximated by f_X2(t) with the
same entropy. Can you please give some references, weblink or source code
discussing this technique? Thank you very much.
--
Yan ZHANG
http://www.nict.com.sg/zhang/
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| | From: | Hiu Chung Law | | Subject: | Re: same entropy between two probability distribution functions. | | Date: | 20 Jan 2005 18:19:38 GMT |
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| In sci.stat.math Yan ZHANG wrote:
> Suppose that a non-negative random variable X follows probability density
> function f_X(t). Since f_X(t) is too complicated, I would like to
> approximate f_X(t) by simpler function f_X2(t) such as exponential or
> hyper-exponential distribution.
> I was once suggested that f_X(t) can be approximated by f_X2(t) with the
> same entropy. Can you please give some references, weblink or source code
> discussing this technique? Thank you very much.
> --
> Yan ZHANG
> http://www.nict.com.sg/zhang/
I would be surprised if approximation by entropy is a good idea.
Anyway, there is too little information to make a useful suggestion,
because the forms of f_X(t) and f_X2(t) are unknown.
You may want to check out variational method which finds the
"best" f_X2(t) within a given family to approximate f_X(t)
with respect to KL divergence.
P.S. Less relevant newsgroups have been removed from "Followup-To".
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