Statistical inference for the shape parameter change-point estimator in negative associated gamma distribution

In this paper, the change-point estimator for the shape parameter is proposed in a negative associated gamma random variable sequence. Suppose that X-1,...,X-n are negative associated random variables satisfying that X-1,...,X-[n tau 0] are identically distributed with Gamma(x; nu(1), lambda), and that X[n tau 0]+1 ,...,X-n are identically distributed with Gamma(x; nu(2), lambda); the change point tau(0) is unknown. The weak and strong consistency, and the weak and strong convergence rate of the change-point estimator, are given by the CUSUM method. Furthermore, the O-P convergence rate of the change-point estimator is presented under the local alternative hypothesis condition.