Abstract

Several methods of finding interval estimators of the parameters of the gamma distribution are considered in the literature. In this work we compare the following methods: Wald confidence intervals; profile likelihood intervals; Bayesian intervals using the Jeffreys prior, the reference prior when α is the parameter of interest and β the nuisance parameter, the reference prior when β is the parameter of interest and α the nuisance parameter; and three fiducial methods. The comparison is done using Montecarlo simulations, in terms of the coverage probabilities and the expected lengths of the intervals, considering small, medium and large sample sizes. As an important result of the simulations we found that the fiducial methods are the best when the sample size is very small, and as the sample size increases all the methods, except the Wald confidence intervals, have a similar behavior. An example of application is shown considering earthquake data of Mexico.

摘要

文献中考虑了几种寻找伽马分布参数的区间估计量的方法。在这项工作中，我们比较以下方法： Wald 置信区间；剖面似然区间；使用 Jeffreys 先验的贝叶斯区间，当α是感兴趣的参数且β是干扰参数时的参考先验，当β是感兴趣的参数且α时的参考先验干扰参数；和三种基准方法。考虑小、中和大样本量，使用蒙特卡洛模拟在覆盖概率和预期间隔长度方面进行比较。作为模拟的一个重要结果，我们发现当样本量非常小时，基准方法是最好的，并且随着样本量的增加，除了 Wald 置信区间之外的所有方法都具有类似的行为。考虑到墨西哥的地震数据，显示了一个应用示例。