Finite Fourier Probability Distribution and Applications

Abstract

A probability distribution is developed to describe data collected from processes that are diffusion driven, in addition to data sets in which the range of the random variable has a fixed lower bound, a fixed upper bound, or both. Chemical equilibrium relationships constrain some data such as water hardness to a fixed lower limit, while chemical solubility relationships establish a fixed upper bound to other water quality data. The solution of a 1D diffusion equation subject to an impulse loading of mass can be adapted as a probability distribution. In this study, the focus is on the solution of the diffusion equation using the integral transform technique when the solution range is 0 ⩽