where μij is the expected number of migration flows between origin i and destination j. Pi and Pj are the populations for i and j, respectively. dij is the distance between representative points in I and j, and {λ, λO, λD, β} are parameters to be estimated. Assuming that observed migration flows follow a Poisson distribution with μij as the expected flows, and are independent of other migration flows, the observed flows, mij, have the probability: