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The Trans-Gompertz Function: An Alternative to the Logistic Growth Function with Faster Growth
1Department of Mathematics, Hampton University, Hampton, VA, USA. fpkozusko@yahoo.com.
Acta Biotheoretica
|July 5, 2015
Summary
The Trans-Gompertz function exhibits faster growth and a larger inflection point ratio compared to the Generalized Logistic function when growth characteristics are matched. This analysis aids in selecting appropriate growth models.
Area of Science:
- Mathematical modeling
- Biostatistics
- Growth curve analysis
Background:
- Growth curves are essential for modeling biological and economic processes.
- The Generalized Logistic function is a widely used growth model.
- The Trans-Gompertz function is a recently developed alternative.
Purpose of the Study:
- To compare the growth characteristics of the Trans-Gompertz function and the Generalized Logistic function.
- To determine which function exhibits superior growth dynamics under specific conditions.
Main Methods:
- Both functions were defined by one shaping and one rate parameter.
- Functions were matched at a specific point on the growth curve.
- First and second derivatives were equated for matching.
Main Results:
- The Trans-Gompertz function demonstrated a faster growth rate.
- The Trans-Gompertz function exhibited a larger inflection point ratio.
- Matched functions revealed distinct growth trajectories.
Conclusions:
- The Trans-Gompertz function offers advantages in modeling rapid growth phases.
- The choice of growth function impacts the interpretation of growth dynamics.
- Further research should explore applications of the Trans-Gompertz function.
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