Reparametrização da distribuição Poisson inflacionada em zero : estimação e aplicação

Abstract

The present work addresses the estimation of the mean of the Zero-Inflated Poisson (ZIP) distribution using the methods of Maximum Likelihood Estimation (MLE) and Moments. A new parameterization for the Zero-Inflated Poisson, named ZIPM, was proposed, introducing the mean (μ) and inflation (δ) parameters. The main objective was to investigate the estimation effectiveness for the mean of the Zero-Inflated Poisson distribution and the suitability of the proposed new parameterization. The results demonstrated that both MLE and the method of moments produced satisfactory estimates for the mean of the ZIPM distribution. No significant differences were found between the methods in terms of estimated mean, mean squared error (MSE), and relative bias. Furthermore, the new ZIPM parameterization showed promise, allowing for refined control of the mean and inflation. However, it is important to note that certain specification errors can occur when using ZIPM and estimation methods. Model adequacy and the validity of estimates depend on meeting underlying statistical assumptions and the data adhering to the Poisson distribution. In conclusion, this work contributes to the field of statistics by proposing the ZIPM parameterization and exploring estimation methods for the mean of the ZIP distribution. The encouraging results indicate the utility of the new parameterization and provide valuable insights for researchers dealing with zero-inflated data. Nevertheless, caution is necessary when interpreting results, considering potential model limitations and associated specification errors.