A note on the fluctuation of flows under the entropy principle

The present paper examines two neglected issues: fluctuation of flows and probability of occurrence, in entropy-based spatial interaction analysis. Variance of the estimated flow is derived to study its fluctuation. It is shown that unless a lower level of accuracy is acceptable, entropy estimates may not be appropriate especially when the scale of a spatial interaction system is small. It is further shown that the probability of having the most probable distribution under the entropy principle is in fact very small. These two findings shed light on the application of entropy-based models.