Poisson regression is often used to analyze trade data. The practice is to add many country export/import dummies to replace the multi-resistance term. The shortage is that the estimation speed could be very low. When providing the gradient and hessian functions, the estimation speed can be 100 times faster using a maximization solver in softwares such as Gauss or Matlab. These functions can be found via Short Note of Poisson Regression and Generalized Poisson Regression. I also apply the generalized Poisson model to test the dispersion in trade using Rose (2002) and Egger et al. (2011) data. Although the trade volume data looks highly over-dispersed, the estimated dispersion parameter is near 0. The finding justifies the use of simple Poisson regression model. To note that Burger, van Oort, and Linders (2009) find significant overdispersion using different regression model.