On Poisson Moment Exponential Distribution with Associated Regression and INAR(1) Process

Numerous studies have emphasised the significance of count data modeling and its applications to phenomena that occur in the real world. From this perspective, this article examines the traits and applications of the Poisson-moment exponential (PME) distribution in the contexts of time series analysis and regression analysis for real-world phenomena. The PME distribution is a novel one-parameter discrete distribution that can be used as a powerful alternative for the existing distributions for modeling over-dispersed count datasets. The advantages of the PME distribution, including the simplicity of the probability mass function and the explicit expressions of the functions of all the statistical properties, drove us to develop the inferential aspects and learn more about its practical applications. The unknown parameter is estimated using both maximum likelihood and moment estimation methods. Also, we present a parametric regression model based on the PME distribution for the count datasets. To strengthen the utility of the suggested distribution, we propose a new first-order integer-valued autoregressive (INAR(1)) process with PME innovations based on binomial thinning for modeling integer-valued time series with over-dispersion. Application to four real datasets confirms the empirical significance of the proposed model. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.