Log-generalized exponential-Poisson regression model and its application to real data

In this paper, we propose a log-generalized exponential Poisson (LGEP) regression model based on generalized exponential Poisson distribution, and some of its structural properties are derived, including distribution function, density function, quantile function, and survival function. Secondly, we developed maximum likelihood estimation (MLE) for the model parameters estimation, also, performed some simulation analysis for different parameter settings and sample sizes to evaluate the performance of the MLEs by analyzing the mean squared error of the MLEs. Finally, we use two set of experimental data, one on the anesthesia response of guinea pigs, and the second on the percentage body fat in human to examine the performance of the LGEP regression model. The results show that the LGEP regression model provides more reliable results and has a better fit than the log-exponential Poisson, log-generalize exponential, and log-generalize extended exponential regression models. In the first data the proposed model reveals that the dosage of the anesthetic drug was shown to exert a positive effect on guinea pigs sleep duration once it reached an adequate level; also, for the second data, the proposed model suggests that both gender and BMI positively influence the percentage body fat across the subjects.