Beta分布的最短置信区间的粒子群优化算法

据置信区间的含义和Beta分布的特性,最短置信区间问题转化成非线性规划问题。给出了粒子群优化算法解决此问题的方法,通过数值计算,对于给定的置信度0.90和0.95,在样本容量从3到30的范围内,求得了一类特殊的Beta分布参数的区间估计。并对通常方法求得的置信区间的长度与最短置信区间的长度进行了对比分析。结果表明,用最短置信区间来作未知参数的区间估计,将会使估计精度得到显著的提高。

Particle Swarm Algorithm for the Shortest Confidence Interval of Beta Distributions

Based on the definition of the confidence interval and characteristic of beta distribution,the shortest confidence interval problem can be transferred to a nonlinear programming problem.Furthermore,the particle swarm algorithm is presented to solve this non-linear programming problem.A special class of interval parameter estimation of Beta distribution is given,with a sample size from 3 to 30 at the degree of confidence 0.90 and 0.95.A comparison of the length of the minimum confidence interval with that of the confidence interval calculated with conventional methods shows that the adoption of the minimum confidence interval can obviously improve the precision of interval estimation for unknown parameters.