  Applications of machine learning (ML) techniques to operational settings
often face two challenges: i) ML methods mostly provide point predictions
whereas many operational problems require distributional information; and ii)
They typically do not incorporate the extensive body of knowledge in the
operations literature, particularly the theoretical and empirical findings that
characterize specific distributions. We introduce a novel and rigorous
methodology, the Boosted Generalized Normal Distribution ($b$GND), to address
these challenges. The Generalized Normal Distribution (GND) encompasses a wide
range of parametric distributions commonly encountered in operations, and
$b$GND leverages gradient boosting with tree learners to flexibly estimate the
parameters of the GND as functions of covariates. We establish $b$GND's
statistical consistency, thereby extending this key property to special cases
studied in the ML literature that lacked such guarantees. Using data from a
large academic emergency department in the United States, we show that the
distributional forecasting of patient wait and service times can be
meaningfully improved by leveraging findings from the healthcare operations
literature. Specifically, $b$GND performs 6% and 9% better than the
distribution-agnostic ML benchmark used to forecast wait and service times
respectively. Further analysis suggests that these improvements translate into
a 9% increase in patient satisfaction and a 4% reduction in mortality for
myocardial infarction patients. Our work underscores the importance of
integrating ML with operations knowledge to enhance distributional forecasts.
