A Unified Expression of Growth Curves and its Application to Data Analysis

Abstract

This paper discusses a methodology for a unified expression of several historically-known growth curves inspired by the Box-Cox transformation. After describing how we construct our unified growth curve, we analyze a sample data set to show its flexibility for curve-fitting performance. Also, it is exhibited that our model can extract a tendency of growth via numerical differentiation technique and linear regression scheme. Moreover, as a method of stochastic analysis of a data set, we newly introduc e a nonzero-started counting process that involves our unified growth curve as its mean value function. We also show a numerical illustration for a short-term prediction with confidence limits.