Classical and Bayesian inference for the discrete Poisson Ramos-Louzada distribution with application to COVID-19 data

The present study is based on the derivation of a new extension of the Poisson distribution using the Ramos-Louzada distribution. Several statistical properties of the new distribution are derived including, factorial moments, moment-generating function, probability moments, skewness, kurtosis, and dispersion index. Some reliability properties are also derived. The model parameter is estimated using different classical estimation techniques. A comprehensive simulation study was used to identify the best estimation method. Bayesian estimation with a gamma prior is also utilized to estimate the parameter. Three examples were used to demonstrate the utility of the proposed model. These applications revealed that the PRL-based model outperforms certain existing competing one-parameter discrete models such as the discrete Rayleigh, Poisson, discrete inverted Topp-Leone, discrete Pareto and discrete Burr-Hatke distributions.

Automated summary

The present study introduces a new extension of the Poisson distribution using the Ramos-Louzada distribution. Various statistical properties of the new distribution are derived and classical estimation techniques are used to estimate the model parameter. A comprehensive simulation study identifies the best estimation method, and Bayesian estimation with a gamma prior is also utilized. Three examples demonstrate the superiority of the proposed model over existing one-parameter discrete models.