My distribution histogram looks like it is not identically distributed, as in the negative counts have a different shape than the positive counts. Here is an image:
The chart has 800 data points, and the tallest count of 40 is for 0.
I don't know a formal approach, but looking at it, it appears to me it is not identically distributed. My guess is that the negative counts (to the left of 0) are closer to a normal distribution, while the positive counts (to the right of 0) are closer to a Laplace distribution, or have higher kurtosis than the left side.
Is this possible, are there cases where this happens, is there a topic in probability that studies it? Or, is this just my eyes playing tricks on me, or not having enough sample data or some other simple reason?
Thanks in advance for any help.