Non-Linear Confluence Analysis

Non-linear confluence analysis, necessary for the treatment of experimental data when all variables are subject to errors, is considered from the standpoint of the maximum likelihood method. The likelihood function is a product of curvilinear integrals of the respective distribution densities of each point of the curve. For a sufficiently small curvature and a normal error distribution, these integrals are evaluated approximately, resulting in distribution functions of the normal type but with modified weights and shifted experimental points. Thus, a confluent problem is reduced to an ordinary regressional one. Weight modifications and point shifts may be found by means of successive approximations.