基于离散枢轴量的泊松分布参数的精确最短置信区间

The Precise Shortest Confidence Intervals of Poisson Distribution Parameter Based on Discrete Pivotal Quantity

将泊松分布参数的充分统计量的离散型分布函数转化为生存伽马分布函数,以此为枢轴量构造了泊松分布参数的精确置信区间.通过数值模拟,选择合适的置信度组合,得到精确最短置信区间.讨论了大样本下泊松分布参数的近似置信区间的估计精度,验证了精确最短置信区间的计算结果.

This paper convert the discrete distribution function of the sufficient statistics of distribution parameter to to survival Gamma distribution function, which used to be a pivotal quantity to construct accurate confidence intervals of Poisson distribution parameters. Then by numerical simulation, we choose the right combination of confidence, to get the shortest confidence intervals. Lastly we discuss the estimation accuracy of approximate confidence intervals of large sample of Poisson distribution parameters, and verify the results of precise shortest confidence interval.