In this article, we establish a goodness of fit test for exponentiality and normality based on the estimated Renyi information. To construct test statistics two estimators are used as an estimator of Renyi information. The first one is an estimator of Renyi distance in manner of Vasicek entropy estimator. Secondly, we use a new cdf estimator which is proposed by Yousefzadeh and Arghami (2008) to obtain a new estimator of Renyi distance. Critical values of test statistics are computed by Monte Carlo simulations. Simulation results show that the proposed tests compare favorably with the leading competitors.

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