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

Area of Science:

• Statistics
• Probability Theory
• Discrete Distributions

Background:

• The Poisson distribution is a fundamental discrete probability distribution widely used in statistical modeling.
• Extensions of existing distributions are crucial for enhancing modeling capabilities and addressing limitations of simpler models.
• The Ramos-Louzada distribution provides a flexible framework for developing new statistical distributions.

Purpose of the Study:

• To introduce and derive a new extension of the Poisson distribution based on the Ramos-Louzada distribution.
• To investigate the statistical and reliability properties of the proposed distribution.
• To evaluate the performance of the new model against existing discrete distributions.

Main Methods:

• Derivation of statistical properties: factorial moments, moment-generating function, probability moments, skewness, kurtosis, and dispersion index.
• Estimation of model parameters using classical techniques (e.g., maximum likelihood) and Bayesian estimation with a gamma prior.
• A simulation study to compare the efficiency of different estimation methods.
• Application of the new model to real-world data for performance evaluation.

Main Results:

• The new distribution, termed the Poisson-Ramos-Louzada (PRL) distribution, exhibits desirable statistical and reliability characteristics.
• Simulation results indicate the most effective estimation methods for the PRL model parameters.
• Empirical applications show that the PRL-based model provides a better fit and outperforms competing one-parameter discrete distributions.

Conclusions:

• The proposed Poisson-Ramos-Louzada distribution is a valuable addition to the family of discrete probability distributions.
• The PRL model offers enhanced flexibility and performance, making it suitable for various statistical modeling tasks.
• The study validates the utility and superiority of the new distribution through theoretical derivations and practical examples.