# Smoothing frequencies without count data

I have frequency data for different events under two conditions, resulting in sets of frequencies F1 and F2. I would like to normalize the frequencies of events under condition 1 by their frequencies under condition 2. However, there are events that occur in condition 1 but not condition 2, resulting in divide-by-zero problems when I attempt to normalize.

For raw count data, I understand that there are a number of smoothing techniques (e.g. Witten-Bell) that can help sort this out, but I only have the frequencies, not the individual counts. In other words, I have frequencies like {0, 0.1, 0.2, 0.7} which could correspond to counts of {0, 1, 2, 7}, {0, 10, 20, 70}, etc. Are there any algorithms that are able to smooth this type of frequency data?

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I think this question is borderline between Computer Science and Cross Validated (but I confess to knowing nothing about stats and machine learning). If you don't get a good answer here after a couple of days, we can migrate your question to Cross Validated. Do not repost; if you wish your question to be migrated, flag it or reply to this comment. –  Gilles Jan 7 '13 at 23:43
Yes. $\:$ Assume that the counts have the smallest sum that would produce your frequency data. $\:$ (How to do that depends on whether the frequencies were calculated and stored as doubles or something else.)