Firstly appologize for using English. My computer is extremely unreliable.

I got a question which has been confused me for a long time.

The question is to calculate the 95% confidence interval for a curve. I have already learnt how to calculate for a straight line.

The curve could be cumulative distribution funciton, Weibull distribution, log-odds, etc.

For example, the cumulative distribution function (CDF) could be expressed as below:
Y = 1/2 * {1 + erf [(X-mean) / (sd * 2^0.5)]}
where ‘erf ’ is called error function, ‘mean’ and ‘sd’ are the mean value and standard deviation of X, respectively. Y is distributed normally from 0 to 1.

If ‘mean’ and ‘sd’ are known, by varying the value of X we could obtain a series values of Y. Then you could plot a typical CDF graph.


Then I need to calculate the 95% confidence intervals of this plotted curve. Could someone tell me how to do it?

I know it could be solved using MATLAB, Minitab, etc. But I want to know the algorithm.

Thank you.