Moment operations on random variables, with applications for probabilistic analysis

A general method is developed for conducting simple operations on random variables, avoiding difficult integrals and singularities, which must be overcome when obtaining exact solutions. For sum, difference and product operations, and combinations thereof, exact moments are first determined from the moments of the constituent variables. The method of orthogonal expansion, developed in the previous paper [Probabilistic Engineering Mechanics 2000;15:371–379], is then used to produce approximate probability density functions (PDFs). The quotient operation is also considered; it requires knowledge of the negative moments of the denominator variable. The quotient and difference operations are used in a first example to establish PDFs for the hazard quotient and excess wind loading on a concrete chimney. A second example demonstrates how the proposed method may be used as an alternative to Monte Carlo simulation for simple probabilistic risk calculations; a PDF for predicted contaminant concentration at a groundwater well compares favorably with a histogram obtained by simulation.