# Confidence interval on entropy estimation

Over a sample (of about a hundred observations), I have estimated the "empirical" entropy of a sequence of identically independently distributed random variables which have 5 possible outcomes.

I was curious to know if there was a possibility to estimate in some way a confidence interval over this "empirical" entropy calculation (i.e. where true probabilities are replaced by their observed frequencies) ?

Best regards

• I've made a few edits to clear up your question a little, but I couldn't work out what to do with the singular/plural mismatches in "a repeated i.i.d. random variables"; please edit to clarify. Apr 8 '14 at 9:33
• You can compute a confidence interval of most things by bootstrapping. Does that help? Apr 8 '14 at 9:37
• @ Glen_b: thank's for the edit I have modified the question hopefully in accordance with your comment. Best regards Apr 8 '14 at 12:55
• @ Adam Ryczkowski : I was more looking at some "asymptotic normality" kind of results, but this approach might work, I have to gie ti a try. Best regards Apr 8 '14 at 12:56
• (When referring to someone with the @ sign make sure that there is no space between it and the user's name. Otherwise SE ignores it and people do not get alerted about the ongoing conversation). Apr 8 '14 at 13:02