Computer aided method for construction of kinetic models of chemical reactions, based on application of chebyshev-hermite polynomials

Abstract

A new method for determination of sampling parameter distribution density p( σ) is presented. This method does not use the linearization procedure of the initial kinetic model in the decision process over the numeric values of σ i (parameters). In essence the method consists in constructing the sampling distribution density of the non-linear model in a form according to the biorthogonal system for Chebyshev-Hermite polynomials. Besides, the selection processes for the random vector of observations, which is indispensable for the calculation of the decomposition coefficients, are generated by the statistical model method. Based on the sampling distribution density obtained in this way, we can take fundamental decisions about the numeric values of the parameters, correct the initial model and apply more effectively the experimental design methods for the precise estimations. In particular, and according to the elective distribution density, not only the exact estimations of maximum likelihood are calculated, but also the confident intervals and domains.