Abstract: A goodness of fit test is constructed by means of empirical Euclidean likelihood,and the limit null distribution of the test statistics is derived.Then,the parameters are estimated by maximum likelihood estimate (MLE) under the composite null hypothesis.Subsequently,the corresponding test statistics is constructed and its limit null distribution is given.Finally,the newtest is compared with chi-square test and Kolmogorov-Smirnov (KS) test by simulations.Simulation results show that the new test is more powerful and has smaller computational complexity.Therefore,the new test shows favorable application and potential prospect.

Key words: empirical Euclidean likelihood, goodness of fit, limitdistribution