Random Forest creating normal distribution out of not normal data Im experiementing with machine learning and my target vairable has a distribution shown below

Not your standard normal distribution. When I train a random forest model on it the predictions from the model follows the below distribution

which is not the same sort of distribution at all. I was under the impression that random forest models are robust to having data which isnt normally distributed? Is it because my training dataa doesnt have enough representation in the extremes? Any thoughts how I can correct this would be great
 A: The point of a machine learning model isn't to output the same distribution, it's to minimize prediction error. Of course, if the prediction error is zero for every input, then the input and output distributions will be the same, but this reasoning doesn't work the other way around. Discrepancy in input and output distribution just implies that the model is imperfect; the degree of mismatch might characterize some amount of model misfit, but that's best measured by the usual statistics such as mean squared error, etc.
If the prediction error of this model isn't small enough for your needs, then you'll need to do some combination of make a better model, collect more data, or gather more informative features.
A: Prediction models aim to answer questions about conditional distributions, (P(y|X)), not about marginal distributions (P(y)).  As others have posted before just looking at marginal distribution of predicted and true data is not sufficient to say anything about the quality of a model. As a simple toy example consider random sampling from the target distribution as a 'model' -- then the marginal plots will almost perfectly match, yet your model is only doing random predictions.
FWIW the distribution of marginal labels suggests there are 2-3 groups of observations, characterized by your features hopefully, that make up the marginal distributions you observe.  This comes from the fact of 2-3 bumps in what looks like a mixture distribution of $P(y) = \sum_{j=1}^{J} P(y | S=s_j) \cdot P(S = s_j)$, where $S$ is some hidden state.  Ideally your features map to those states, i.e., $P(S | X)$ is not independent.
A: Random forests are robust to having data which isn't normally distributed but that doesn't mean that the predictions won't be pulled to the natural center of your data to minimize the rmse.
Looks like your features may not be good enough to partition the data to follow the real distribution so you should look at getting better features or doing some feature engineering.
Edit to add some more thoughts:
It does look like your target is made of a mixture distribution which can be visibly seen.  So you may want to look into separating the two distributions and look for any correlations, may reveal some useful insights that you may not be accounting for in the model.
