I have an experimentally observed distribution that looks very similar to a gamma or lognormal distribution. I've read that the [lognormal distribution](http://en.wikipedia.org/wiki/Log-normal_distribution) is the maximum entropy probability distribution for a random variate $X$ for which the mean and variance of $ln(X)$ are fixed. Does the gamma distribution have any similar properties?

What methods can I use to determine the true PDF of my data?