On 09/06/2013 5:42, Rich Ulrich wrote: > 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?
Now I got the point: Sergio was talking about the CI for a quantile, while I understood that the Sergio's Y was an estimate of the population mean. Sorry for the inconvenience.