In the present paper, we use the already defined alpha-divergence and gamma-divergence for constructing some goodness of fit tests for exponentiality. These divergence measures are very robust with respect to outliers. Since the existence of outliers among statistical data can be lead to misleading results, therefore utilizing these divergence measures can be of impor- tance. In order to construct test statistics, two estimators are used for alpha-divergence and gamma-divergence. In the first one, we consider the alpha-divergence and gamma-divergence of the equilibrium distribution function, which is well defined on the empirical distribution function -EDF- and is proposed as an EDF-based goodness of fit test statistic. The second one is an estimator in manner of Vasicek entropy estimator. Simulation results indicate that in comparison with the other tests statistics, our mentioned test statistics almost in most of the cases have higher power. Finally, two examples containing outliers illustrate the impor- tance and use of the proposed tests.

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