Lagrange had given two expansions for a function towards the end of the eighteenth century, but they were used very little. Good (1955, 1960, 1965) did the pioneering work by developing their multivariate generalization and by applying them effectively to solve a number of important problems. However, his work did not generate much interest among researchers, possibly because the problems he considered were complex and his presentation was too concise.
The Lagrange expansions can be used to obtain very useful numerous probability models. During the last thirty years, a very large number of research papers has been published by numerous researchers in various journals on the class of Lagrangian probability distributions, its interesting families, and related models. These probability models have been applied to many real life situations including, but not limited to, branching processes, queuing processes, stochastic processes, environmental toxicology, diffusion of information, ecology, strikes in industries, sales of new products, and amounts of production for optimum profits.