Modelling flight delays with negative values Modelling flight delays with negative values
I am working on a model to predict whether a flight will be delayed. The data consists of some explanatory variables for flights from a specific airport. I initially thought modelling this as count data would be a good idea, but as pointed out in the comments that is misleading.
The response variable is the number of minutes deviations from departure initial departure time. I have some explanatory variables about the flights to work with, i.e. date, distance traveled, etc.. I don't have any weather variables though.
The following is the histogram of the data. I have a positively skewed distribution and I am thinking what kind of a distribution would be a good candidate to model this.

I am now asking, what kind of model is appropriate for this kind of data? The main goal is to do predictions. 
One idea I had was to train a classifier first to determine whether the flight will be delayed or not and then predict how late it would become with a regressions model, but I would also like to predict how early it went if that is the case.
I think that I will use logistic regression to predict whether a flight will be late or early and then construct a prediction model for these two classes. What ideas do you have for models that would be good to predict deviation from set take-off time conditioned on that it will be a delayed take-off or an early take-off? 
Edited to remove my confusions about count data.
 A: First, I agree that this is not count data. 
If there are many flights that are canceled, then you might think of it as time to event data and look into survival analysis methods. This might depend on where and when you are: More flights are cancelled from Chicago in winter than from Phoenix in May. 
Other than that, you might try quantile regression; I suggest this for two reasons: First, you might be particularly interested in long delays. If you are interested in this from a passenger POV, then a short delay in departure might not matter at all - these are often made up during the flight, and I think most passengers are more concerned with arrival time than departure time. But if you are the airport manager, then even a short delay might be a problem with scheduling runways and so on.  Quantile regression lets you model the quantiles. Second, quantile regression makes no assumptions about the distribution of the residuals.
For the early departures, I think you have to figure out whether an early departure is better or worse or equivalent to an on-time departure.
