Shape of a distribution as a feature
If this distribution is row specific (each sample has a different associated distribution) or category specific this is not a bad approach to encode more information in your features. It's unclear how you have these distributions, are there empirical samples or do you have a parameterized distribution? A few approaches you could take to encoding this could be:


Fit a distribution family (or if you have one already) and use the location/shape/scale parameters as features
Add a few moments and other statistics of the distribution
Or similarly take a few percentiles


Depending on the parameterization of the distribution, the first might be less direct but it should be easy to test.