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I'm looking to sample a probability distribution function (let's call it $F$) where the frequencies of the different (discrete) events are collected empirically. Since it is collected empirically, I do not have a closed-form expression for $F$.

If $F$ instead was known in closed-form, then we could use the inverse transformation method $Y=F(X)$, where $Y\sim U(0,1)$, in order to get $X=F^{-1}(Y)$.

Perhaps one could do curve fitting and then apply the inverse transformation method, but this sounds a bit prone to errors. Also, if the fitted curve is complicated, then doing the inverse might become tricky. Is there another idea I'm not aware of?

Thanks in advance for your help.

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  • Select at random from the stream of events? – BruceET Mar 22 '17 at 16:18
  • Not sure I follow. If the events have different probabilities of occuring, then how will selection with uniform probability help? – index Mar 22 '17 at 16:21
  • Different definitions of 'event'. I mean 'subjects' or 'indicents'. Suppose each 'customer' (subject) may purchase nothing or several items. Then your 'event' might be the actual number X purchased. Sample customers at random and you simulate the distribution of X. Or subjects might be of different religions (A, B, C, ..., Other). Sample subjects at random and you approx the probabilities of various religions in pop from which they come. // If this isn't feasible, maybe explain the process by which your prob dist'n arises. Hope there are random incidents or subj somewhere in the background. – BruceET Mar 22 '17 at 18:08

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I think I found the answer on pp. 8-8 and 8-9 in: http://web.ics.purdue.edu/~hwan/IE680/Lectures/Chap08Slides.pdf

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