1
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.