Abstract

Transcendental models are often solved by using a different approach, which can be a derivative free, direct optimisation or iterative linearization method. All these approaches require guess values for the unknown parameters to start the iteration procedure. However, if the transcendental model involves several parameters, some of these methods become very cumbersome and computationally expensive. A new method for computing parameter estimates which are then used as initial values for the unknown model parameters to start the iteration process was proposed. Confidence intervals for the estimated parameters were constructed using the bootstrap method. We generated two randomised datasets that simulated the decay and growth processes. A three parameterized single exponential model  was identified using the simulated datasets in each case. The absolute percentage errors were used as a measure of comparison between the proposed method and the current Levenberg-Marquardt (L-M) method. Tables and figures were used to present results from both methods. The proposed method appeared to produce better results than the current L-M method. The superiority of the proposed method over the current methods is that it does not require initial guess values and it guarantees convergences. Thus the proposed method could be adopted to solve real life problems.

Key words: Least-squares, parameter identification, transcendental models, confidence intervals, bootstrap method, initial guess values, Gaussian white noise, probability model.