Monotonic decrease of upper limit estimated with Gompertz model for data described using logistic model
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The Gompertz curve and logistic curve models are often used to forecast upper limits (saturation points). To accurately estimate an upper limit, an appropriate model selection as well as accurate parameter estimation is required. We mathematically analyze how an upper limit estimated with an inappropriate model changes as the data size increases, i.e., time elapses, when the Gompertz curve model is selected for data described on the exact solution of the logistic curve model. We prove that an estimated upper limit is strictly monotonically decreasing as the historical data size increases and that the upper limit estimated with the inappropriate model converges to the upper limit estimated with the appropriate model as the data size approaches infinity. These results can help in selecting an appropriate model.
KeywordsGompertz curve model Logistic curve model Model-selection Applied discrete systems Discrete equation Exact solution
Mathematics Subject Classification39A60 62J05 91B62
We thank anonymous reviewers for their careful reading and helpful comments.
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