MONTE-CARLO METHOD FOR THE DETERMINATION OF CONFIDENCE-INTERVALS - ANALYSIS OF NONNORMALLY DISTRIBUTED ERRORS IN SEQUENTIAL EXPERIMENTS

The Monte Carlo method for determining confidence intervals for optimized values of the adjustable parameters derived from a model for fitting a set of experimental data is extended to the case where one or more fixed parameters are transferred from the analysis of a previous experiment. For the case of nonlinear models, the distributions characterizing the fixed parameters are not normal so that a basic assumption underlying the usual methods of parametric statistics is not satisfied. Since the Monte Carlo method presented here is simply an implementation of the definition of confidence intervals, the method is applicable regardless of the nonlinearity of the model or of covariances between parameters. The method is illustrated by means of an example involving the determination of equilibrium constants and molar absorptivities using spectrophotometry.