# How does one quantify the difference between two distributions, especially if sample sizes differ?

I have plotted some experimental data of mine, and these data points fall into the following distributions:

So, these are fairly non-trivial looking distributions. I would like to figure out methods to quantify how these distributions differ. Perhaps a Kullback-Leibler divergence?

What other methods could I use to do this? There's also a question of how to deal with differing levels of sparsity/different sample sizes.

• A qq-plot is always a useful comparison. – Alex R. Mar 29 '17 at 18:45
• @AlexR. How would one do this for these distributions? – ShanZhengYang Mar 29 '17 at 18:49

You cannot treat your $Q$ distribution as it is treated canonically in the definition. A bit of statistical manipulation to your data will be necessary. Your options are 1. Subsample according to a uniform increment $P$ so that it can align with $Q$ or 2. you can interpolate pairs of points in $Q$ so that a subdivision can be instantiated to extrapolate more data points.