Properties of Gompertz data revealed with non-Gompertz integrable difference equation

Abstract

Abstract Behaviour of the upper limit estimated by an unsuitable model (the logistic curve model) was mathematically analysed for data on an exact solution of the Gompertz curve model with integrable difference equations. The analysis contributes to identifying a suitable model because the behaviour is independent of noise included in actual data. A suitable model is indispensable for correct forecasts. The following results were proved. The estimated upper limit monotonically increases as the data size increases and converges to the upper limit estimated with the suitable model (the Gompertz curve model) as the data size approaches infinity. Therefore, the upper limit estimated with the logistic curve model is smaller than that estimated with the Gompertz curve model.