至多一个变点的Γ分布的统计推断及在金融中的应用

INFERENCE AND APPLICATION IN FINANCE OF Γ-DISTRIBUTION WITH AT MOST ONE CHANGE-POINT

对至多一个变点的Γ分布,即X1,X2…,Xn为一列相互独立的随机变量序列,且X1,X2,…,X[nΥ0]i．i．d～Γ(x;ν1,λ1),X[nΥ0]+1,X[nΥ0]+2,…,Xn i．i．d～Γ(x;ν2,λ2),其中Υ0未知,称Υ0为该序列的变点．在利用第一型极值分布逼近文中提出统计量的分布的基础上,给出了变点Υ0估计(?)的相合性及强弱收敛速度．最后给出了在金融序列上的应用．

In this paper the change point of parameter in Γ- distribution is considered Suppose that X1,X2,…,X（nτ0）＋1…,Xn are independent random variables where X1,X2,…,X[nτ0]i.i.d- Γ（x;v1,λ1）,and X[nτ0] ＋2,…,Xn,i.i.d-Γ（x;v2,λ2）,τ0 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.