How to plot confidence bounds for a theoretical cumulative distribution function?
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I understand how to plot upper and lower confidence bounds for an experimental cumulative distribution function using the ecdf function.
But how to plot upper and lower confidence bounds for a theoretical cumulative distribution like for example the Theoretical CDF in the plot shown below? (copied from: https://www.mathworks.com/help/stats/cdfplot.html)
Jeff Miller on 6 Aug 2021
For a given X value, the theoretical cumulative probability is p = F(X). Suppose you have a sample of N observations and you let k be the number of observations <= X. k is (by definition) binomial(N,p) with the known N and that theoretical p. Using that binomial distribution, you can get upper and lower confidence limits on the observed k (e.g., with a normal approximation to the binomial). Then divide those upper and lower lilmits on k by N and you will have upper and lower confidence limits on p for that X value.