Problem of distinguish between distributions is always important. It is become more complicate when data is contaminated by outliers. Here, we use two well known Lindley and exponential distributions infected by outliers. Closeness of the Lindley distribution in comparing with exponential distribution with outliers is discussed in this research. Three ways such as likelihood ratio, asymptotic likelihood ratio tests and minimum Kolmogorov distance are used to select the proper fitted model for a real data set. We perform Monte Carlo simulation to obtain the probability of correct selection (PCS) for varies values of sample sizes and parameters based on the best criteria in the distributions. In general, it has been seen that the Lindley distribution is closers to exponential distribution contaminated by outliers based on the likelihood ratio and Kolmogorov criteria. An actual example of real data is used to see the behavior of the distributions.

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