Predicting the scoring time in hockey

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.