I have a dataset and I made the QQ-plot against the $N(0,1)$ distribution. The plot is included below.
My statistics is rusty to say the least (meaning what little knowledge I had is now rusted away!) Clearly the normal distribution is not a good fit -- the tails in my data are heavier than those in a normal distribution. But the data appears not to be skewed relative to the normal distribution.
So, which distribution might be a better fit? Is it something a transformation like Box-Cox could cure to make it fit better?
My data isn't strictly positive so Box-Cox is out... But there may be another transformation that works.
I have increasingly large datasets and I need to see what, if anything, the datasets converge to. This is exploratory analysis, I would rather find a distribution that fits the data rather than transforming the data to a distribution. All of this is done with SciPy which reports the asymptotic value of the biased kurtosis as -1 and skewness as 0.
But I don't know how to use that information to determine which distribution this might be, aside from checking all of them to see which ones give a better $r^2$.
Based on a comment from gung, I checked it against a uniform distribution:
Sure enough, that's considerably better although still shows a difference in the tails.