Property of Gompertz data through convex of upper limit estimated with logistic difference equation

The Gompertz curve and logistic curve models are often used to forecast the upper limit. An appropriate model-selection method as well as accurate parameter estimation is required to obtain an accurate estimation of the upper limit. Upper limits estimated with the logistic curve model as an inappropriate model were proved to be upward convex after a certain data size for data described on the exact solution of the Gompertz curve model. This was accomplished by using a difference equation that has the exact solution. The appropriate model-selection method with the properties of estimated upper limits that are upward convex and already obtained monotonic increase was applied to three actual datasets. These properties help us to select an appropriate model between the Gompertz curve and logistic curve models.