[(An algorithm for determining values of parameters of the Gompertz growth function)].

Abstract

In the literature some attempts were made to analyse and to construct models for biological growth processes and to describe the quantitative aspects of a growth characteristic's changes in time using the Gompertz' function y=aexp(-exp(b--ct)). In this paper differential equations are derived having the Gompertz' function as solution. The goodness of fit after adjusting a chosen analytical expression to the courses of measured values is able to give hints at the reliability of that expression as a true model. This possibility of verification was hardly practiced in past because of lacking in proper numerical procedures for performing the nonlinear regression. An ALGOL program for iterative adjusting the parameters of the GOMPERTZ' function (with or without a constant term) to measured values is given in an appendix of the present paper. Starting values for the nonlinear parameters b and c will be evaluated by Internal Least Squares using one of the derived differential equations. For this algorithm an ALGOL program is given in the appendix too. The growth of human embryo serves as an example to demonstrate the numerical procedures and related programs for evaluating the starting values of the parameters and for their iterative improvement until reaching a minimum for the remainding variance between calculated and measured courses.