Forest fires are one of the biggest ecological disasters in Canada. Counts and sizes of fires vary substantially from year to year. In this study, the data is collected from Northwest Territories in Canada. We assume that fire counts appear to follow the Gamma-Poisson distribution, and fire sizes approximately follow the Gamma-Exponential distribution. The Maximum Likelihood Estimation and Random Search are used to estimate the parameters of two models. Identifiability issues regarding parameters in the two models are explored. The Kolmogorov–Smirnov test is used to check for goodness of fit. For fire sizes data, although the Kolmogorov–Smirnov test shows a low p-value, by plotting theoretical and empirical distribution, we can see that the Gamma-Exponential distribution fits adequately.