The cumulative distribution function of the Two Parameter Poisson Xgamma is given by:
$$
F(x)=1-\frac{1}{2(\alpha+\theta)(1+\theta)^{x+3}}\left((x^2+5x+6)\alpha \theta^2+2(x+3)\alpha \theta
+2(1+\theta)^2+2\alpha \right)
$$
References
"Wani, M. A., Ahmad, P. B., Para, B. A. and Elah, N. (2023). A new regression model for count data with applications to health care data. International Journal of Data Science and Analytics."