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Topic: A "plausible range" for a random variable
Replies: 9   Last Post: Jun 11, 2013 7:42 PM

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 Richard Ulrich Posts: 2,961 Registered: 12/13/04
Re: A "plausible range" for a random variable
Posted: Jun 11, 2013 7:37 PM

On Tue, 11 Jun 2013 11:25:20 -0700 (PDT), andrea.panizza75@gmail.com
wrote:
...
me>>
>> The theory for the CI is that you can estimate the variance
>> of a transformation of X by taking the right derivative.

>
>Hmmm, surely I'm missing something here. Right derivative? I thought that the theory of CI was to find the asymptotic distribution of an estimator.

I read what you extracted here, and I said to myself,
"What the hell was I talking about?" and "What is CI"?

After I re-read a few sentences before, I realized that
I should have been less terse, as follows:

"The theory that I was using before when computing the
CI makes use of the fact that calculus gives us a
procedure for (often) estimating the variance of a
linear or nonlinear transformation, based (usually)
on the original mean and variance. For the Poisson,
the result of taking the square root is that the SD of
the transformation is a constant, 0.5." (That is a
one of the facts that I draw on most often when reading
technical news or scientific reports. It is handy, to assess
the error terms that often iare not well-reported.)

>
> This

>> works out as follows. From that estimate, the standard
>> deviation of the sqrt(Poisson) = 1/2 (approximately).
>> And the distribution of the sqrt(Poisson) is very close to
>> normal, once the counts are above a few.

You can read more the complicated versions of this, at

http://en.wikipedia.org/wiki/Propagation_of_uncertainty

--
Rich Ulrich