We propose two goodness of ft test statistics based on Cumulative Kullback–Leibler (CKL) information and Cumulative residual Kullback–Leibler (CRKL) information for exponential distributions with unknown parameter and randomly censored data. Koziol and Green introduced the Cramér-von Mises statistics with randomly censored data for a simple hypothesis based on the Kaplan–Meier product limit of the distribution function. We use their idea to obtain test statistics based on CKL and CRKL for a randomly censored exponential distribution with estimated parameters. The power of the proposed tests for testing exponentiality is compared with the test statistics based on the empirical distribution function using the opinion of Koziol and Green. A simulation study is performed under a special censorship model introduced by Koziol and Green. Simulation studies show a relatively high power of proposed test statistics in many alternatives.

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