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.

本文针对两参数负二项分布（two-parameter negative binomial distributions）的置信区间（confidence intervals, CIs）与预测区间（prediction intervals, PIs）构建问题展开研究。针对该分布的均值，本文提出了若干基于大样本方法的简易置信区间，并将其与似然置信区间（likelihood CIs）进行对比。所提简易置信区间不仅计算简便，且在中等样本量场景下的性能优于似然置信区间。此外，本文还针对来自两参数负二项分布的未来样本均值，提出了对应的预测区间并对其精度进行评估。最后通过两个实际数据集案例对所提方法进行实例演示。