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Discrete Gompertz equation and model selection between Gompertz and logistic models

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  • Satoh, Daisuke

Abstract

A discrete Gompertz model and model selection between the Gompertz and logistic models are proposed. The proposed method utilizes the difference between the regression equations for the proposed and the discrete logistic models. The difference is whether the log of both sides is taken or not. The proposed discrete model has higher goodness-of-fit for actual data than the non-homogeneous Poisson process Gompertz model that is commonly used in software reliability engineering. The proposed model selection method is simpler than an existing method based on the mean relative squared error, because the proposed method requires only the correlation coefficients between variables on regression equations for both discrete Gompertz and logistic models. It yields absolutely correct selection when pseudo-data are on exact solutions of the Gompertz and logistic models. Also, it yields correct results earlier than the existing model selection for actual data.

Suggested Citation

  • Satoh, Daisuke, 2021. "Discrete Gompertz equation and model selection between Gompertz and logistic models," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1192-1211.
    • Handle: RePEc:eee:intfor:v:37:y:2021:i:3:p:1192-1211
    DOI: 10.1016/j.ijforecast.2021.01.005
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    References listed on IDEAS

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