On Discrete Poisson–Mirra Distribution: Regression, INAR(1) Process and Applications

Several pieces of research have spotlighted the importance count data modelling and its applications in real-world phenomena. In light this, a novel two-parameter compound-Poisson distribution is developed this paper. Its mathematical functionalities are investigated. The two unknown parameters estimated using both maximum likelihood Bayesian approaches. We also offer parametric regression model for datasets based on proposed distribution. Furthermore, first-order integer-valued autoregressive process, or INAR(1) used to demonstrate utility suggested time series analysis. conditional likelihood, least squares, Yule–Walker techniques. Simulation studies innovative undertaken as an assessment long-term performance estimators. Finally, we utilized three real depict new model’s applicability.