On Sun, 09 Jun 2013 01:10:54 +0200, Cristiano <cristiapi@NSgmail.com> wrote:
>On 07/06/2013 19:31, Rich Ulrich wrote: >> Poisson consideration gives a good approximation for small >> proportions. This is applied for your N=2000, 2 1/2%, as follows. >> >> Rank 50 is the point estimate of L. The +/- 2SD range for Poisson >> can be estimated as ( Square(Sqrt(L) - 1), Square(Sqrt(L) + 1) ) >> >> The square root of 50 is about 7; the square of 6 is 36, and the >> square of 8 is 64. That gives (approximately) the CI for L=50 >> is (37, 65). > >When the sample is taken in N(0,1), using your limits for N= 2000 I get >a 73% confidence level. Is that the intended level?
For a sample Xi, i=1,n (=2000) you have R1 ... Rn, X's sorted in rank order, so that Ri < Rj for i<j
The point estimate for 5% two tailed extreme results are the values of (R50, R1950) where R1950 is R(2000-50), simply applying symmetry.
The CI around the value for R50 are the values in (R37, R65) . Similarly, for the other end (symmetry).
Where do you see a 73% confidence level? Do you see whatever you were doing wrong?
> >That CI doesn't seem good for other distributions (uniform, exponential, >log-normal and weibull), because I get 0 or 100%. Am I wrong?
This non-parametric approach is sound. Whatever you were doing was not what I *intended* to prescribe. My apologizies, if I previously was too terse. I've give a *bit* more detail this time.