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We propose here a general statistic for the goodness-of-fit test of statistical models. The proposed statistic is constructed based on an estimate of Kullback–Leibler information. The properties of the proposed test are stated and then the established results are used to introduce goodness-of-fit tests for the normal and exponential distributions. A simulation study is carried out for examining the power of the proposed test and to compare it with those of some existing procedures. Our study shows that the proposed test is superior to the competitors in most of the considered cases and can confidently apply in practice. Finally, some illustrative examples are presented and analysed, and concluding comments are made.

A new estimator of Kullback–Leibler information based on a local linear regression and its application in goodness-of-fit tests