BACKGROUND: Determination 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.
RESULTS: A 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.
CONCLUSION: This 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.