几何分布置信限推导

Deduction of Fiducial Limit with Geometric Distribution

设总体Y^Ge(p),P未知.现有Y的n个独立随机样本Y_i,i=1,2,…,n,记Q=∑nt=1Y_i,则Q服从负二项分布.根据几何分布与负二项分布的关系并结合数学分析的工具推导出P的双侧置信限.

This paper probes chiefly into the confidence interval of parameters by means of the method of mathematical analysis.It is assumed that Y ~Ge(p),and p is unknown.Now there are n independent random samples such as Y_i,i = 1,2,…,n.Let Q=∑nt=1Y_i,thereforeQ complies with the negative binomial distribution.On the basis of the relationship between geometric distribution and negative binomial distribution,combined with the tools of mathematical analysis,this paper deduces the bilateral fiducial limit of the parameter p.