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A new one-parameter discrete length-biased exponential distribution called the discrete moment exponential (DMEx) distribution is introduced using the survival discretizing approach. We derive the reliability measures including survival function, hazard function, residual reliability function, and the second rate of failure function. Further, the mathematical properties of the DMEx distribution are derived. The parameters of the DMEx distribution are estimated using seven estimation methods. A simulation study is carried out to explore the behavior of the proposed estimators. It is observed that the maximum likelihood approach provides efficient estimates. Finally, the DMEx is adopted for fitting the number of COVID-19 deaths in China and Europe countries. It is shown that the DMEx distribution fits the data better than other competing discrete distributions.
Afify et al. (Sat,) studied this question.