  In this paper, we propose a Bayesian predictive density estimator to predict
the time until the r-th goal is scored in a hockey game, using ancillary
information such as their performances in the past, points and specialists'
opinions. To be more specific, we consider a gamma distribution as a waiting
scoring model. The proposed density estimator belongs to an interesting new
version of weighted beta prime distribution and outperforms the other estimator
in the literature. The efficiency of our estimator is evaluated using
frequentist risk along with measuring the prediction error from the old
dataset, 2016-17, to the current season (2018-19) of the National Hockey
League.
