基于生存贝塔分布的几何分布参数精确区间估计  

Accurate interval estimation of geometric distribution parameter based on survival beta distribution

作　　者：徐玉茹[1] 徐付霞[1] 

机构地区：[1]天津工业大学理学院,天津300387

出　　处：《哈尔滨商业大学学报（自然科学版）》2016年第5期588-592,共5页Journal of Harbin University of Commerce：Natural Sciences Edition

摘　　要：证明了几何分布参数的充分统计量服从负二项分布,由此将负二项分布转化为生存贝塔分布,构造出了参数的精确置信区间,并且在不同的置信度组合中选出最佳组合,得到精确最短置信区间.讨论了大样本下几何分布的近似区间估计,通过数值模拟,直观展示区间估计的精度变化,说明了精确最短区间估计的优良性.This paper proved that the sufficient statistic of a geometric distribution parameter is subjected to the negative binomial distribution. Therefore,constructed the exact confidence interval of the parameter by converting the negative binomial distribution into the survival beta distribution,and select the best combination in different levels of the confidence to get the accurate shortest confidence interval of its parameter. The approximate interval estimate under the large sample of a geometric distribution was discussed in this paper. Through numerical simulation,the change of the accuracy of an interval estimation was intuitively demonstrated,and then the superiority of the accurate shortest confidence interval was illustrated.

关 键 词：几何分布 负二项分布 贝塔分布 精确置信区间 渐进正态性 

分 类 号：O212.5[理学—概率论与数理统计]