Modified information criterion for regular change point models based on confidence distribution

In this article, we propose procedures based on the modified information criterion and the confidence distribution for detecting and estimating changes in a three-parameter Weibull distribution. Corresponding asymptotic results of the test statistic associated the detection procedure are established. Moreover, instead of only providing point estimates of change locations, the proposed estimation procedure provides the confidence sets for change locations at a given significance level through the confidence distribution. In general, the proposed procedures are valid for a large class of parametric distributions under Wald conditions and the certain regularity conditions being satisfied. Simulations are conducted to investigate the performance of the proposed method in terms of powers, coverage probabilities and average lengths of confidence sets with respect to a three-parameter Weibull distribution. Corresponding comparisons are also made with other existing methods to indicate the advantages of the proposed method. Rainfall data is used to illustrate the application of the proposed method.