中文摘要：

研究了在先验分布为贝塔分布下，负二项分布未知参数θ的贝叶斯区间估计方法。借助Beta分布与F分布的关系给出了参数θ的一般后验区间估计，并给出了参数θ的最短后验区间估计的条件极值解法。通过对参数取值不同的密度曲线形状的讨论分析和数值实例对比，得出结论：在小样本情况下，最短置信区间估计方法值得采用。

英文摘要：

In terms of prior distribution of Beta distribution, the Bayesian estimation method on the unknown parame-ter θ of negative binomial distribution was studied. By means of the relations between Beta distribution and the F dis-tribution the general posterior interval estimation of parameter θ was given, and the shortest posterior interval estima-tion by means of conditional extreme was gained. By comparing the discussion analysis and numerical examples den-sity curve shape of the different parameters, it was concluded that in the case of small samples, the shortest confi-dence interval estimation method is worth using.