In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. First, preliminary results on these problems are presented. Next, we compare the risk functions of the Bayes estimators based on the truncated and untruncated beta priors and obtain dominance conditions when the probability parameter is smaller than a known constant. Finally, our problem is shown to be related to a similar problem in the Poisson case.

翻译：在本文中,我们考虑贝叶斯点估测和预测密度估测,首先,介绍这些问题的初步结果。接下来,我们根据短短和未修补的贝塔前科比较拜叶斯估计者的风险功能,并在概率参数小于已知常数时获得支配地位条件。最后,我们的问题与Poisson案中的类似问题有关。