A New Generalization of Geometric Distribution with Properties and Applications

In this study, a new two-parameter mixed-Poisson distribution is proposed. Statistical properties of the proposed distribution are studied comprehensively. The maximum likelihood estimation method is used to estimate unknown model parameters. A simulation study is conducted to evaluate the asymptotic efficiencies of the maximum likelihood estimators of model parameters. The usefulness of proposed distribution is demonstrated in first-order integer-valued autoregressive process, shortly INAR(1). Empirical findings show that the proposed INAR(1) process provides better results than other competitive models when the time series of counts display over-dispersion.