Abstract
In this paper, the change-point estimator for the shape parameter is proposed in a negative associated gamma random variable sequence. Suppose that are negative associated random variables satisfying that are identically distributed with , and that are identically distributed with ; the change point 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 convergence rate of the change-point estimator is presented under the local alternative hypothesis condition. MSC:62F12, 62G10.
Highlights
The gamma distribution occurs frequently in a variety of applications, especially in reliability, in survival analysis and in modeling income distributions
The density of a gammadistributed random variable X with a shape parameter ν and a scale parameter λ is given by f (x; ν, λ) = λν xν– e–λxI (x > ), ( )
When the shape parameter ν =, the gamma distribution is an exponential distribution with parameter λ; when λ
Summary
The gamma distribution occurs frequently in a variety of applications, especially in reliability, in survival analysis and in modeling income distributions. The shape parameter is especially of interest in reliability theory because the gamma distribution is either a decreasing failure rate (DFR), a constant or an increasing failure rate (IFR) according to whether the shape parameter is negative, zero or positive. There is a considerable body of literature on change-point analysis that assume that the random variables being considered are independent.
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