In this talk, we shall introduce two parameterized deformation of the classical Poisson random variable from the viewpoint of noncommutative probability, namely $(q, s)$-Poisson type operator on the two parameterized deformed Fock space, namely, the $(q, s)$-Fock space constructed by the weighted $q$-deformation approach. The recurrence formula for the orthogonal polynomials of the $(q, s)$-deformed Poisson distribution is determined. Moreover we shall also give the combinatorial moment formula of the $(q, s)$-Poisson type operator by using the set partitions and the card arrangement technique with their statistics. Our method presented in this talk provides nice combinatorial interpretations to parameters, $q$ and $s$.