I have a target variable that has the following distribution. I have tried the typical regression models such as logistic regression, ridge regression, catboost regression etc. but I'm thinking that I could use a model that takes into account the features but also some kind of prior knowledge of the distribution of the target variable. Im trying to predict duration in minutes and I’m trying to use machine learning to predict that. Some of my features might have normal or other distributions but do not really know how to use even that. Any suggestions?
You're looking at the marginal, not the conditional, and regression makes assumptions about the conditional.
It seems like your outcome is bounded below by 0, so you may want to choose a likelihood which supports this (e.g. exponential or gamma). It also seems like the outcome is bounded above by 40. Is that true? If so, rescale so the outcome is on [0,1] and consider beta regression.
if for any theoretical reasons your values can only range between a known minimum (0 in your case) and a known maximum (40 in your case or another value, say 100) you can rescale them to be between 0 and 1 and use fractional logistic regression. If there is no mass at 0 and 1 the beta function (beta regression) could also be a choice.
I hope it helps