International Journal of Nonlinear Analysis and Applications

Closeness of Lindley distribution to an exponential distribution with the presence of outliers

Document Type : Research Paper

Authors

1 Department of Statistics, Payame Noor University of Tehran, Tehran-Iran

2 Department of Statistics, Ferdowsi University of Mashhad, Mashhad-Iran

Abstract

The problem of distinguishing between distributions is always important. It becomes more complicated when data is contaminated by outliers. Here, we use two well-known Lindley and exponential distributions infected by outliers. The closeness of the Lindley distribution in comparison with the 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 for various 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 closer 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 behaviour of the distributions.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 7
July 2025
Pages 185-193
  • Receive Date: 11 March 2021
  • Revise Date: 18 August 2023
  • Accept Date: 16 October 2023