Diffusion-Based Semi-Infinite Fourier Probability Distribution

Abstract

A multitude of natural processes occurring in environmental and water resources are diffusive processes, and their observations exhibit a natural lower bound of zero and practically no upper bound. Such processes can be modeled using a dye diffusion equation whose solution yields a concentration distribution. This function, when normalized, leads to a two-parameter probability distribution that is seen to be a superposition of two normal distributions. Parameters of this distribution were estimated by the methods of moments and maximum likelihood for Monte Carlo-generated processes.