Polynomial approaches in improving accuracy of probability distribution estimation using the method of moments

Abstract Background Determination of a probability density function is an area of active research in engineering sciences as it can improve process systems. A previously developed polynomial method‐of‐moments‐based probability density function estimation model has been applied in the research to produce accurate approximations to both standard and more complex probability density functions. A model with a different polynomial basis than monomial is still to be developed and evaluated. This is the work that is undertaken in this study. Results A set of standard probability density functions (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 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. This article is protected by copyright. All rights reserved.