Novel Discrete Chris–Jerry Distribution: Properties, Integer Autoregressive Process, and Applications

A unique one‐parameter discrete distribution, known as the Poisson Two‐Sum Chris–Jerry distribution, is proposed in this study. The structural properties of the contemporary distribution, such as index of dispersion, moments, and probability‐generating function, are determined. To obtain the estimates of the parameter, the maximum likelihood estimation procedure is used. The performance of the estimation technique on finite samples is assessed through a comprehensive simulation study. The formulated distribution is further used to develop an integer autoregressive process for modeling autocorrelated count data. The usefulness of the new distribution and its autoregressive process are demonstrated by modeling some count data and their performances compared with other existing competing discrete distributions. The results show that both the distribution and its autoregressive process can serve as alternative models for count data modeling.