In a recent study to improve the patient ﬂows at a local hospital, data of the patients’ length of stay at PACU need to be analyzed to ﬁt into diﬀerent theoretical distributions to be used in mathematical and simulation models. However, due to the irregularity of the data, normal software that comes with the simulation package cannot ﬁnd a theoretical distribution for the data. In this project, we want to model the distribution of observed staying time statistically. Specifically, we consider a mixture model of two gamma distribution. We use expectation-maximization (EM) algorithm to find the parameter estimates and use bootstrap method to obtain the variance and consequently the confidence interval of the parameters.