A non-negative integer-valued model: Estimation, count regression and practical examples

In this study, we propose a non-negative integer-valued model based on the sum of Poisson-Lindley and geometric distributions. We show that it corresponds to weighted distribution also special mixture two negative binomial distributions with certain parameters. The main statistical properties new are studied comprehensively, including estimation parameter. A count regression analysis is introduced by using distribution. Finally, provide some applications practical data sets.