“…As for the crime data, can be considered as the number of re-offendings provoked by with probability . Depending on the nature of this kind of observed data, the INAR(1) models have been modified and generalized with respect to their orders (Ristić and Nastić [ 3 ], Nastić, Laketa and Ristić [ 4 ]), dimensions (Pedeli and Karlis [ 5 ], Khan, Cekim and Ozel [ 6 ]), marginal distributions (Alzaid and Al-Osh [ 7 ], Alzaid and Al-Osh [ 8 ], Jazi, Jones and Lai [ 9 ], Ristić, Nastić and Bakouch [ 10 ], Barreto-Souza [ 11 ]), thinning operators (Ristić, Bakouch and Nastić[ 12 ], Liu and Zhu [ 13 ]), and mixed models (Ristić and Nastić [ 3 ], Li, Wang and Zhang [ 14 ], Orozco, Sales, Fernández and Pinho [ 15 ]). For more literature, we refer to review papers (Weiß [ 16 ], Scotto, Weiß and Gouveia [ 17 ]).…”