Generalizing growth functions assuming parameter heterogeneity.

Abstract

This paper describes generalizations of simple growth equations made by assuming that one or more parameters have a probability distribution in the population. Thus, the product of the parental growth equation and the probability density function when integrated over the range of the parameter produces a compound growth function. In most cases, the resulting equations are more complex than the original function, but the new parameters are interpretable directly in terms of the distribution of the parameter in the population. Despite the frequent need for special functions, an effort has been made here to produce simple mathematical forms. An example is provided using some compound growth functions to describe real growth data. This method appears to be a meaningful and useful way to improve the modeling of growth.