Polynomial Approaches in Improving Accuracy of Probability Distribution Estimation Using the Method of Moments

Abstract

BACKGROUNDDetermination of a probability density function (PDF) is an area of active research in engineering sciences as it can improve process systems. A previously developed polynomial method-of-moments-based PDF estimation model has been applied in the research to produce accurate approximations to both standard and more complex PDF. A model with a different polynomial basis than a monomial is still to be developed and evaluated. This is the work that is undertaken in this study.RESULTSA set of standard PDF (Normal, Weibull, Log Normal and Bimodal) and more complex distributions (solutions to the Smoluchowski coagulation equation and Population Balance equation) were approximated by the method-of-moments using Chebyshev, Hermite and Lagrange polynomial-based density functions. Results show that Lagrange polynomial-based models improve the fit compared to monomial based-modeling in terms of RMSE and Kolmogorov-Smirnov test statistic estimates. The Kolmogorov-Smirnov test-statistics decreased by 19% and the RMSE values were improved by around 85% compared to the standard monomial basis when using Lagrange polynomial basis.CONCLUSIONThis study indicates that the procedure using Lagrange polynomials with method-of-moments is a more reliable reconstruction procedure that calculates the approximate distribution using lesser number of moments, which is desirable. (c) 2024 The Authors. Journal of Chemical Technology and Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry (SCI).