This kind of coupling relation takes on a double-exponential function changing law, and the evolutive track of the interaction between urbanization and eco-environment is a double-exponential curve.

There are three different CV models that including the two-parameter hyperbolic model, the three-parameter hyperbolic model and the three-parameter exponential model.

In this paper, we used the concepts of the maximum likehood estimate and the direction maximum likehood estimate to give two kinds of estimates for two-parameter exponential distribution.