InvQMOM: A Simple Inversion Method that Works

01.Jan.2021

​We present a universal inversion method to reconstruct the underlying probability density function (pdf) and its cumulative distribution (cdf) from the embedded information in the quadrature nodes and weights of QMOM. These nodes and weights are evolved according to the kinetics governing the interactions among the particles of the dispersed phase such as nucleation, condensation, evaporation, splitting and aggregation. This pdf is represented by a dynamic histogram supported with moving bin boundaries. The inverted pdf and cdf are general and free of any prior assumption about the type of the distribution. We called this method “InvQMOM” which is supposed to converge to the exact pdf and cdf as the number of quadrature nodes increases. The order of convergence of the inverted pdf is O(h²) and O(h³) for cdf, where h is the spacing between the two quadrature nodes that encompass the node from which the point functional value is reconstructed.

https://www.researchgate.net/publication/353323774_InvQMOM_A_Simple_Inversion_Method_that_Works​