In this paper, we consider prediction for the exponential distribution with unknown location. For the most part, we treat the one-dimensional case and assume that the location parameter is restricted to an interval. The Bayesian predictive densities with respect to prior densities supported on the real line and the restricted space are compared under the Kullback–Leibler divergence. We first consider the case where the scale parameter is known. We obtain general dominance conditions and also minimaxity and admissibility results. Next, we treat the case of unknown scale. In this case, the location parameter is assumed to be less than a known constant and sufficient conditions for domination are obtained. Finally, we treat a multidimensional problem with known scale where the location parameter is restricted to a convex set. The performance of several Bayesian predictive densities is investigated through simulation. Some of the prediction methods are applied to real data.

在本文中，我们考虑对未知位置的指数分布进行预测。在大多数情况下，我们处理一维情况并假设位置参数限于一个区间。在 Kullback-Leibler 散度下比较了在实线和受限空间上支持的先验密度的贝叶斯预测密度。我们首先考虑尺度参数已知的情况。我们获得了一般优势条件以及极小极大和可容许性结果。接下来，我们处理规模未知的情况。在这种情况下，假设位置参数小于已知常数，并且获得了支配的充分条件。最后，我们处理一个已知尺度的多维问题，其中位置参数仅限于凸集。通过模拟研究了几个贝叶斯预测密度的性能。一些预测方法适用于真实数据。