A new one-parameter discrete exponential distribution: Properties, inference, and applications to COVID-19 data

A new one-parameter discrete length-biased exponential distribution called the discrete moment expo-nential (DMEx) distribution is introduced using the survival discretizing approach. We derive the relia-bility 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 sim-ulation 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. (c) 2022 The Author(s). Published by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

This paper introduces a new one-parameter discrete length-biased exponential distribution called the discrete moment exponential (DMEx) distribution using the survival discretizing approach. The reliability measures of the DMEx distribution are derived, and the parameters are estimated using seven estimation methods. A simulation study demonstrates that the maximum likelihood approach provides efficient estimates. Finally, the DMEx distribution is adopted to fit the number of COVID-19 deaths in China and Europe countries, showing a better fit compared to other competing discrete distributions.