Confidence intervals and prediction intervals for two-parameter negative binomial distributions

Problems of finding confidence intervals (CIs) and prediction intervals (PIs) for two-parameter negative binomial distributions are considered. Simple CIs for the mean of a two-parameter negative binomial distribution based on some large sample methods are proposed and compared with the likelihood CIs. Proposed CIs are not only simple to compute, but also better than the likelihood CIs for moderate sample sizes. Prediction intervals for the mean of a future sample from a two-parameter negative binomial distribution are also proposed and evaluated for their accuracy. The methods are illustrated using two examples with real life data sets.

本文聚焦两参数负二项分布（two-parameter negative binomial distributions）的置信区间（Confidence Intervals, CIs）与预测区间（Prediction Intervals, PIs）求解问题。文中提出了若干基于大样本方法的两参数负二项分布均值简易置信区间，并将其与似然置信区间（likelihood CIs）进行对比分析。结果显示，所提置信区间不仅计算过程简便，在中等样本量场景下的表现亦优于似然置信区间。此外，本文还针对来自两参数负二项分布的未来样本均值构建了预测区间，并对其预测准确性开展了评估验证。最后，通过两个实际数据集实例对所提方法进行了演示说明。