%0 Journal Article
%T INFERENCE AND APPLICATION IN FINANCE OF $\Gamma$-DISTRIBUTION WITH AT MOST ONE CHANGE-POINT<br>至多一个变点的$\Gamma$分布的统计推断及在金融中的应用
%A Tan Changchun
%A Zhao Lincheng
%A Miao Baiqi
%A <br>谭常春
%A 赵林城
%A 缪柏其
%J 系统科学与数学
%D 2007
%I 
%X In this paper the change point of parameter in ${\it \Gamma}$- distribution is considered. Suppose that $X_{1}, X_{2}, \cdots ,X_{n\tau_{0}]},X_{n\tau_{0}]+1},\cdots,X_{n}$ are independent random variables where $X_{1},X_{2}, \cdots ,X_{n\tau_{0}]}$ i.i.d $\sim {\it \Gamma}(x;\nu_{1}, \lambda_{1}),$and $X_{n\tau_{0}]+1}, X_{n\tau_{0}]+2},\cdots, X_{n}\ {\rm i.i.d} \sim {\it \Gamma}(x;\nu_{2}, \lambda_{2}),\ \tau_{0}$ is unknown and called change point. The distribution of the statistic proposed in the paper can be approximated by the first type of extremal distribution . Under mild conditions, the strong consistency and rate of convergence of the estimator for the change point are presented. At the same time, its application are also presented.
%K $\Gamma$-distribution
%K change point
%K strong consistency
%K rate of convergence<br>Γ分布
%K 变点
%K 强相合估计
%K 收敛速度
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=32A78E0FAB5A029F&yid=A732AF04DDA03BB3&vid=DB817633AA4F79B9&iid=CA4FD0336C81A37A&sid=0B39A22176CE99FB&eid=F3090AE9B60B7ED1&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=17