I am dealing with a set of data that appears to follow a gamma distribution or a lognormal distribution but the only issue is that the data set is in percentages and both of these distributions don't work with 0 or very near 0 values. My question is would there be anything wrong about multiplying the entire data set by 100 or 1000, and then fitting the distribution?

Also if anyone knows of a better way to fit near zero values to a distribution (i.e. %s) please let me know.


Multiplying by 1000 would only change the scale parameter (of either the gamma or lognormal); if it didn't fit before you multiplied by 1000 it won't fit any better after. So that's not help at all.

If you have exact zeros, no continuous distribution on the positive half-line will really address that problem.

I'd suggest considering a zero-inflated distribution (essentially a mixture of exact 0's and whatever continuous distribution is reasonable for the rest of it). Zero-inflated gammas seem to crop up reasonably often.

You may also have an issue if those percentages can't exceed 100%, because neither the gamma nor the lognormal are bounded like that; in that case you might consider a zero-inflated beta. If 100% is possible, there's also a 0/1-inflated beta.

As for how to model "near-zeros" that entirely depends on what those near-zeros behave like. You haven't given any information on which to base a suggestion of a model -- we'd only be guessing. It may be that an additional mixture component for very small values might help.

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