I'm trying to get my own excel sheet to calculate the confidence limits or belts.
I'm interesting in apply it to the Two Components Extreme Values (TCEV) Distribution for Flood Frequency Analysis and the Gumbel (Tipe I) distribution.
But for a practical validation I'm using the only soft that I found that calculate a confidence interval: Cumfreq (http://www.waterlog.info/cumfreq.htm).
The instructions says they calculate the Confidence intervals by means of the standard deviation (Sd) of the binomial probability distribution: Sd=sqrt{Fc(1-Fc)/N}, where Fc is the cumulative (non-exceedance) frequency, and N is the number of data. Also they uses the t-statistic with a 90% confidence equal to 1.7 if N is longer than 10 as a factor to assign Sd to the upper or lower limits (see figure 1
), and so the Upper limit is: U=Fc + 2x1.7 Fc Sd and the lower one is : L=Fc - 2x1.7(1-Fc)Sd.
With only that information I don't know exactly how to reach to the output of the program in an example. When I don't know if the Sd refers to all the distribution or to the probability of any data as we can see in figure 2 
, and with the formula I obtain a different value in the first case (not equal to 0.51). Also, if I sopose the 0.51 St.Dev, I obtain others limits (U and L) different of 2.0 and 0.3.
The graphic method that they refer in the website (http://www.waterlog.info/pdf/freqtxt.pdf) doesn't help me, we can see a particular nomograph, not for cumulative curve but for other interesting curve of the return period. And it does not explain the numeric example.
Other article that can help me is this: Oosterbaan, R.J. 1988. Frequency predictions and their binomial confidence limits. But I don't find this or any explanation based on exercises for find the confidence belt or prediction intervals based in the binomial distribution to frequency analysis. There are a lot for the confidence analysis of regression between two variables, but not so many to frequency fitting.
Could someone provide me with any example or the formulas to get the values that fit the output of Cumfreq?
Other useful formulas can be the methodology that refer wikipedia, by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood. But I need a clear example of the methodology with a simple theory reference, not the contrary.
Thank you very much if you can give me some steps or examples to deal with it.
Finally I encontered the solution.
Only one have to follow the instruction of the software and use the fraction results when applying the formulas. Fc will be the result of apply the Gumbel equation to any x value. Not the % values.
Thanks in any way.