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Discrete Gompertz equation and model selection between Gompertz and logistic models
International Journal of Forecasting ( IF 6.9 ) Pub Date : 2021-02-08 , DOI: 10.1016/j.ijforecast.2021.01.005
Daisuke Satoh

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.



中文翻译:

离散Gompertz方程和Gompertz与逻辑模型之间的模型选择

提出了离散的Gompertz模型,并提出了Gompertz模型与Logistic模型之间的模型选择。所提出的方法利用了所提出的和离散逻辑模型的回归方程之间的差异。区别在于日志双方是否被采取。与软件可靠性工程中通常使用的非均匀泊松过程Gompertz模型相比,所提出的离散模型具有更高的实际数据拟合优度。所提出的模型选择方法比基于均值相对平方误差的现有方法更简单,因为所提出的方法仅需要离散Gompertz模型和logistic模型的回归方程变量之间的相关系数。当伪数据位于Gompertz和Logistic模型的精确解上时,它将产生绝对正确的选择。而且,它比实际数据的现有模型选择更早产生正确的结果。

更新日期:2021-02-08
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