On Tue, 11 Jun 2013 11:25:20 -0700 (PDT), email@example.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