A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise
A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise
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DOI：
10.3390/math7060541
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发表时间：
2019-06-01
期刊：
影响因子：
2.4
通讯作者：
Torres-Ruiz, Francisco
中科院分区：
文献类型：
--
作者：
Roman-Roman, Patricia;Jose Serrano-Perez, Juan;Torres-Ruiz, Francisco
许多动态真实的现象的行为表现出不同的阶段，每一个都遵循S型模式。这需要研究具有多个拐点的S形曲线。在这项工作中，引入了一个扩散过程，其平均函数是这种类型的曲线，具体地说，在其表达式中引入一个多项式项后，著名的Gompertz模型的变换。研究了模型参数的极大似然估计，并给出了在处理真实的情况时选择多项式次数的各种准则。最后给出了一些仿真实例。
The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is introduced whose mean function is a curve of this type, concretely a transformation of the well-known Gompertz model after introducing in its expression a polynomial term. The maximum likelihood estimation of the parameters of the model is studied, and various criteria are provided for the selection of the degree of the polynomial when real situations are addressed. Finally, some simulated examples are presented.