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Monotonic decrease of upper limit estimated with Gompertz model for data described using logistic model

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Abstract

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.

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Acknowledgements

We thank anonymous reviewers for their careful reading and helpful comments.

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  1. NTT, 3-9-11 Midori-cho, Musashino-shi, Tokyo, 180-8585, Japan

    Daisuke Satoh & Ryutaro Matsumura

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  1. Daisuke Satoh
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  2. Ryutaro Matsumura
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Correspondence to Daisuke Satoh.

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Satoh, D., Matsumura, R. Monotonic decrease of upper limit estimated with Gompertz model for data described using logistic model. Japan J. Indust. Appl. Math. 36, 79–96 (2019). https://doi.org/10.1007/s13160-018-0333-9

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  • DOI: https://doi.org/10.1007/s13160-018-0333-9

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