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A simple method is proposed to detect the number of change points in a sequence of independent exponential family random variables. An estimator to maximize some criterion, say SC(k), which is to maximize the log-likelihood function with some penalty term, is used in detection. Under some mild assumptions, the consistency of the estimator for the true number of change points and the boundedness between the estimated change locations and the true change location are obtained. Some simulated results are given, and the Nile problem is investigated by this method.

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