Identifying distribution of a variable Consider a variable that can take both negative and positive values, and that has the following density plot:

I am trying to identify the distribution of this variable. The density plot resembles that of a Gamma distribution. However, since the variable can take negative values, it certainly does not follow a Gamma distribution.
What is the best guess as to the distribution of this variable? Of course, the next step would be to plot a QQ plot of the sample quantiles v.s. the theoretical quantiles of the "guessed" distribution.
Any help would be appreciated. Thank you!
 A: Are you sure that you need a parametric density function in the first place? If you want to sample from the distribution, I would suggest increasing the bandwidth parameter on the density estimator to make the estimation more smooth. I don't think you should ever be forced to say "this variable follows X parametric distribution" in what you are doing. 
You could consider the best density function as the one that minimizes some error metric (MSE, MAE, etc). You would compare each data point of your actual distribution to the parametric density function to get these values. In general, there is no correct density function and you can fit almost any distribution you want to any set of data. Standardizing the variable might be a good idea: subtract the mean and divide by the standard deviation. Or, just shift your variable to the right as per the comment.
A: A gamma distribution that is standardized as you describe can still be thought of as a gamma distribution if we include a third parameter for the location (starting point). 
That is, suppose $X \sim \mathrm{Gamma}(k,\theta),$ where $k$ is the shape parameter and $\theta$ is the scale parameter (this is the same as Wikipedia's first parameterization for a gamma distribution). 
Let $Y=X-\mu,$ where $\mu=k\theta$ is the mean of $X.$ Then $Y \sim \mathrm{Gamma}(k,\theta,-\mu),$ where the $-\mu$ indicates the distribution starts at $-\mu$ rather than at $0.$ 
Finally, let $Z = {{X-\mu} \over {\sigma}},$ where $\sigma = \sqrt{k} \theta,$ the standard deviation of $X.$ Then $Z \sim \mathrm{Gamma}\left(k,{\theta \over \sigma},{-\mu \over \sigma}\right).$ This can be simplifed to $Z \sim \mathrm{Gamma}\left(k,{1 \over \sqrt{k}},{-\sqrt{k}}\right) $ 
Your case may differ since it appears you used sample mean and sample standard deviation to do your standardization rather than population parameters. But the same method applies - if you started with gamma variates, you still have gamma variates - just shifted and scaled. 
