至多一个变点的Γ分布的统计推断

Inference in Γ-distribution With at Most One Change-point

对至多一个变点的Γ分布,即X1,…,Xn为一列相互独立的随机变量序列,且X1,…,Xk0 i.i.d～Γ(x;ν1,λ1),Xk0+1,…,Xn i.i.d～Γ(x;ν2,λ2),其中k0未知,称k0为该序列的变点.借助Gauss过程理论和滑窗方法,利用第一型极值分布逼近本文提出的统计量的分布,给出了检测变点k0的程序和变点的区间估计.最后对文中提出的统计量进行模拟并分析.

Let X 1,…,X k 0 ,X k 0+1 ,…,X n be independent random variables such that X 1,…,X k 0 i.i.d~Γ(ν 1,λ 1) and X k 0+1 ,…,X n i.i.d~Γ(ν 2,λ 2 ).k 0 or k 0/n is called change-point.In this paper the change-point of Γ-distribution with two parameters is discussed.With the help of the theory of Gaussian process and the method of slipping window,the distribution of the statistics proposed can be approximated by the first type of extremal distribution.The detection procedures are also proposed by the statistics presented.