伽玛分布参数的最短置信区间

Shortest Confidence Interval of Parameter of Gamma Distribution

Γ(β,θ)分布中未知参数θ的最短置信区间实际上是一个条件极值问题,它能转化成一个方程组可用数值方法迭代求解。在假设参数β=1,置信水平为0.95的条件下,比较了常用置信区间与最短置信区间的长度,结果表明:两者长度的绝对差d(n)和相对差e(n)均随样本容量n的增大而减小,当n≤9时,e(n)≥10%。这说明在小样本下,研究参数的最短置信区间是必要的。

The shortest confidence interval of parameter of Gamma distribution is in practice a question of conditional extremum. It can be＇transferred to a group of equations that can be solved by a method of numerical value. Assume β=1 , and confidence level is 0.95, the length of normal confidence interval is compared to the length of shortest confidence interval, the results show： both absolute difference d（ n） and relative difference e（ n） are decreased by the increasing sample number n, when n ≤9, e（n） ≥ 10%. So it is necessary to research the shortest confidence interval of parameter for small samples.